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95-402: The Franck–Condon principle has a well-established semiclassical interpretation based on the original contributions of James Franck . Electronic transitions are relatively instantaneous compared with the time scale of nuclear motions, therefore if the molecule is to move to a new vibrational level during the electronic transition, this new vibrational level must be instantaneously compatible with

190-749: A quantum dot such as a small sphere confines in three dimensions, a quantum wire confines in two dimensions, and a quantum well confines only in one dimension. These are also known as zero-, one- and two-dimensional potential wells, respectively. In these cases they refer to the number of dimensions in which a confined particle can act as a free carrier. See external links , below, for application examples in biotechnology and solar cell technology. The electronic and optical properties of materials are affected by size and shape. Well-established technical achievements including quantum dots were derived from size manipulation and investigation for their theoretical corroboration on quantum confinement effect. The major part of

285-503: A 1926 Physical Review article titled "A Theory of Intensity Distribution in Band Systems". Here he formulates the semiclassical formulation in a manner quite similar to its modern form. The first joint reference to both Franck and Condon in regard to the new principle appears in the same 1926 issue of Physical Review in an article on the band structure of carbon monoxide by Raymond Birge . Consider an electrical dipole transition from

380-437: A collision. In order for a molecule to break apart, it must acquire from the photon a vibrational energy exceeding the dissociation energy, that is, the energy to break a chemical bond. However, as was known at the time, molecules will only absorb energy corresponding to allowed quantum transitions, and there are no vibrational levels above the dissociation energy level of the potential well . High-energy photon absorption leads to

475-543: A concert Franck met Ingrid Josephson, a Swedish pianist. They were married in a Swedish ceremony in Gothenburg on 23 December 1907. They had two daughters, Dagmar (Daggie), who was born in 1909, and Elisabeth (Lisa), who was born in 1912. To pursue an academic career in Germany, having a doctorate was not enough; one needed a venia legendi , or habilitation. This could be achieved with either another major thesis or by producing

570-538: A curves in Diagram I. the particles will have a potential energy greater than D' and will fly apart. In this case we have a very great change in the oscillation energy on excitation by light... James Franck recognized that changes in vibrational levels could be a consequence of the instantaneous nature of excitation to higher electronic energy levels and a new equilibrium position for the nuclear interaction potential. Edward Condon extended this insight beyond photoreactions in

665-595: A family of rabbis. Franck attended primary school in Hamburg. Starting in 1891 he attended the Wilhelm-Gymnasium , which was then a boys-only school. Hamburg had no university then, so prospective students had to attend one of the 22 universities elsewhere in Germany. Intending to study law and economics, Franck entered the University of Heidelberg in 1901, as it had a renowned law school. He attended lectures on law, but

760-400: A great weakening of the binding on a transition from the normal state n to the excited states a and a ' . Here we have D > D' and D' > D". At the same time the equilibrium position of the nuclei moves with the excitation to greater values of r . If we go from the equilibrium position (the minimum of potential energy) of the n curve vertically [emphasis added] upwards to the

855-463: A higher energy level with 4.9 eV more energy. This means that the electron is more loosely bound to the mercury atom. There were no intermediate levels or possibilities. In a second paper presented in May 1914, Franck and Hertz reported on the light emission by the mercury atoms that had absorbed energy from collisions. They showed that the wavelength of this ultraviolet light corresponded exactly to

950-508: A pair of children from drowning in the Spree River . For his Doctor of Philosophy (Dir. Phil.) under Warburg's supervision, Warburg suggested that he study corona discharges . Franck found this topic too complex, so he changed the focus of his thesis . Entitled Über die Beweglichkeit der Ladungsträger der Spitzenentladung ("On the Mobility of Ions "), it would subsequently be published in

1045-748: A position at the Niels Bohr Institute in Copenhagen . He needed a new collaborator, so he took on Hilde Levi , whose recent thesis had impressed him. His original intention was to continue his research into the fluorescence of vapours and liquids, but under Bohr's influence they began to take an interest in biological aspects of these reactions, particularly photosynthesis , the process by which plants use light to convert carbon dioxide and water into more organic compounds. Biological processes turned out to be far more complicated than simple reactions in atoms and molecules. He co-authored two papers with Levi on

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1140-399: A potential well if sufficient energy is added to the system such that the local maximum is surmounted. In quantum physics , potential energy may escape a potential well without added energy due to the probabilistic characteristics of quantum particles ; in these cases a particle may be imagined to tunnel through the walls of a potential well. The graph of a 2D potential energy function

1235-474: A problem had aroused his interest he was completely captivated, indeed obsessed by it. Common sense and straight logic were his main tools, together with simple apparatus. His research followed an almost straight line, from his early studies of ion mobilities to his last work on photosynthesis; it was always the energy exchange between atoms or molecules that fascinated him. In addition to the Nobel Prize. Franck

1330-538: A specific quantity (4.9  electronvolts ) of its kinetic energy before flying away. A faster electron does not decelerate completely after a collision, but loses precisely the same amount of its kinetic energy. Slower electrons just bounce off mercury atoms without losing any significant speed or kinetic energy. These experimental results provided confirmation of Albert Einstein 's photoelectric effect and Planck's relation ( E = fh ) linking energy ( E ) and frequency ( f ) arising from quantisation of energy with

1425-433: A substantial body of published work. Franck chose the latter route. There were many unsolved problems in physics at the time, and by 1914 he had published 34 articles. He was the sole author of some, but generally preferred working in collaboration with Eva von Bahr , Lise Meitner , Robert Pohl , Peter Pringsheim  [ de ] , Robert W. Wood , Arthur Wehnelt or Wilhelm Westphal . His most fruitful collaboration

1520-480: A transition or prohibit it altogether. Rotational selection rules have been neglected in the above derivation. Rotational contributions can be observed in the spectra of gases but are strongly suppressed in liquids and solids. It should be clear that the quantum mechanical formulation of the Franck–Condon principle is the result of a series of approximations, principally the electrical dipole transition assumption and

1615-434: A transition to a higher electronic state instead of dissociation. In examining how much vibrational energy a molecule could acquire when it is excited to a higher electronic level, and whether this vibrational energy could be enough to immediately break apart the molecule, he drew three diagrams representing the possible changes in binding energy between the lowest electronic state and higher electronic states. Diagram I. shows

1710-744: A wide variety of related phenomena. For his work during this time period, Franck was elected to the American Academy of Arts and Sciences in 1929. This period came to an end when the Nazi Party won power in Germany in an election on 2 March 1933. The following month it enacted the Law for the Restoration of the Professional Civil Service , which provided for the retirement or dismissal of all Jewish civil servants, along with political opponents of

1805-479: Is a potential energy surface that can be imagined as the Earth's surface in a landscape of hills and valleys. Then a potential well would be a valley surrounded on all sides with higher terrain, which thus could be filled with water (e.g., be a lake ) without any water flowing away toward another, lower minimum (e.g. sea level ). In the case of gravity , the region around a mass is a gravitational potential well, unless

1900-489: Is a function of nuclear coordinates. Since the dependence is usually rather smooth it is neglected (i.e., the assumption that the transition dipole surface is independent of nuclear coordinates, called the Condon approximation is often allowed). The first integral after the plus sign is equal to zero because electronic wavefunctions of different states are orthogonal. Remaining is the product of three integrals. The first integral

1995-576: Is applied equally to absorption and to fluorescence . The applicability of the Franck–Condon principle in both absorption and fluorescence, along with Kasha's rule leads to an approximate mirror symmetry shown in Figure 2. The vibrational structure of molecules in a cold, sparse gas is most clearly visible due to the absence of inhomogeneous broadening of the individual transitions. Vibronic transitions are drawn in Figure 2 as narrow, equally spaced Lorentzian line shapes. Equal spacing between vibrational levels

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2090-418: Is determined by the charge (− e ) and locations ( r i ) of the electrons as well as the charges (+ Z j e ) and locations ( R j ) of the nuclei : The probability amplitude P for the transition between these two states is given by where ψ {\displaystyle \psi } and ψ ′ {\displaystyle \psi '} are, respectively,

2185-419: Is illuminated by light corresponding to the electronic transition energy, some of the chromophores will move to the excited state. Within this group of chromophores there will be a statistical distribution of solvent-chromophore interaction energies, represented in the figure by a Gaussian distribution function. The solvent-chromophore interaction is drawn as a parabolic potential in both electronic states. Since

2280-471: Is often labeled as "Solvation Coordinate" and represents, somewhat abstractly, all of the relevant dimensions of motion of all of the interacting solvent molecules. In the original Franck–Condon principle, after the electronic transition, the molecules which end up in higher vibrational states immediately begin to relax to the lowest vibrational state. In the case of solvation, the solvent molecules will immediately try to rearrange themselves in order to minimize

2375-488: Is only the case for the parabolic potential of simple harmonic oscillators, in more realistic potentials, such as those shown in Figure 1, energy spacing decreases with increasing vibrational energy. Electronic transitions to and from the lowest vibrational states are often referred to as 0–0 (zero zero) transitions and have the same energy in both absorption and fluorescence. In a report published in 1926 in Transactions of

2470-433: Is represented as that of a harmonic oscillator, and the spacing between phonon levels ( ℏ Ω i {\displaystyle \hbar \Omega _{i}} ) is determined by lattice parameters. Because the energy of single phonons is generally quite small, zero- or few-phonon transitions can only be observed at temperatures below about 40 kelvins . Franck–Condon considerations can also be applied to

2565-439: Is the region surrounding a local minimum of potential energy . Energy captured in a potential well is unable to convert to another type of energy ( kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to do due to entropy . Energy may be released from

2660-483: Is the solvation contribution to the Stokes shift . James Franck James Franck ( German pronunciation: [ˈdʒɛɪ̯ms ˈfʁaŋk] ; 26 August 1882 – 21 May 1964) was a German physicist who won the 1925 Nobel Prize for Physics with Gustav Hertz "for their discovery of the laws governing the impact of an electron upon an atom". He completed his doctorate in 1906 and his habilitation in 1911 at

2755-457: Is the vibrational overlap integral, also called the Franck–Condon factor . The remaining two integrals contributing to the probability amplitude determine the electronic spatial and spin selection rules. The Franck–Condon principle is a statement on allowed vibrational transitions between two different electronic states; other quantum mechanical selection rules may lower the probability of

2850-445: Is treated as a classical continuum due to the large number of molecules involved. Although emission is depicted as taking place from the minimum of the excited state chromophore-solvent interaction potential, significant emission can take place before equilibrium is reached when the viscosity of the solvent is high, or the lifetime of the excited state is short. The energy difference between absorbed and emitted photons depicted in Figure 7

2945-647: The Annalen der Physik . With his thesis completed, Franck had to perform his deferred military service. He was called up on 1 October 1906 and joined the 1st Telegraph Battalion. He suffered a minor horse riding accident in December and was discharged as unfit for duty. He took up an assistantship at the Physikalische Verein in Frankfurt in 1907, but did not enjoy it, and soon returned to Frederick William University. At

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3040-774: The Franck Report . Finished on 11 June 1945, it recommended that the atomic bombs not be used on the Japanese cities without warning. In any event, the Interim Committee decided otherwise. Franck married Hertha Sponer in a civil ceremony on 29 June 1946, his first wife, Ingrid, having died in 1942. In his post-war research, he continued to tackle the problem of explaining the mechanism of photosynthesis. Meitner saw no break between his early and later work. She recalled that Franck enjoyed talking about his problems, not so much to explain them to others as to satisfy his own mind. Once

3135-901: The Frederick William University in Berlin, where he lectured and taught until 1918, having reached the position of professor extraordinarius . He served as a volunteer in the German Army during World War I . He was seriously injured in 1917 in a gas attack and was awarded the Iron Cross 1st Class. Franck became the Head of the Physics Division of the Kaiser Wilhelm Gesellschaft for Physical Chemistry. In 1920, Franck became professor ordinarius of experimental physics and Director of

3230-628: The Nazi Party came to power in Germany in 1933, Franck resigned his post in protest against the dismissal of fellow academics. He assisted Frederick Lindemann in helping dismissed Jewish scientists find work overseas, before he left Germany in November 1933. After a year at the Niels Bohr Institute in Denmark , he moved to the United States, where he worked at Johns Hopkins University in Baltimore and then

3325-516: The Picardy sector of the Western Front . He became a deputy officer ( offizierstellvertreter ), and then a lieutenant ( leutnant ) in 1915. In early 1915 he was transferred to Fritz Haber 's new unit that would introduce clouds of chlorine gas as a weapon. With Otto Hahn he was responsible for locating sites for the attacks. He was awarded the Iron Cross , Second Class, on 30 March 1915, and

3420-455: The Planck constant ( h ). But they also provided evidence supporting the model of the atom that had been proposed the previous year by Niels Bohr . Its key feature was that an electron inside an atom occupies one of the atom's "quantum energy levels". Before a collision, an electron inside the mercury atom occupies its lowest available energy level. After the collision, the electron inside occupies

3515-488: The University of Chicago , where his work on photosynthesis had attracted interest, in 1938. Franck's first paper there, co-authored with Edward Teller , was on photochemical processes in crystals. Hans Gaffron became his collaborator. They were joined by Pringsheim, who escaped from Belgium after the German invasion . Franck arranged a position for Pringsheim at his laboratory. Both his daughters and their families moved to

3610-660: The University of Chicago . During this period he became interested in photosynthesis . Franck participated in the Manhattan Project during World War II as Director of the Chemistry Division of the Metallurgical Laboratory . He was also the chairman of the Committee on Political and Social Problems regarding the atomic bomb, which is best known for the compilation of the Franck Report , which recommended that

3705-450: The atomic bombs not be used on the Japanese cities without warning. James Franck was born in Hamburg , Germany, on 26 August 1882, into a Jewish family, the second child and first son of Jacob Franck, a banker, and his wife Rebecca née Nachum Drucker. He had an older sister, Paula, and a younger brother, Robert Bernard. His father was a devout and religious man, while his mother came from

3800-406: The electrons and electron holes come closer, and the energy required to activate them increases, which ultimately results in a blueshift in light emission . Specifically, the effect describes the phenomenon resulting from electrons and electron holes being squeezed into a dimension that approaches a critical quantum measurement, called the exciton Bohr radius . In current application,

3895-429: The nuclear positions and momenta of the vibrational level of the molecule in the originating electronic state. In the semiclassical picture of vibrations (oscillations) of a simple harmonic oscillator, the necessary conditions can occur at the turning points, where the momentum is zero. Classically, the Franck–Condon principle is the approximation that an electronic transition is most likely to occur without changes in

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3990-432: The 4.9 eV of energy that the flying electron had lost. The relationship of energy and wavelength had also been predicted by Bohr. Franck and Hertz completed their last paper together in December 1918. In it, they reconciled the discrepancies between their results and Bohr's theory, which they now acknowledged. In his Nobel lecture, Franck admitted that it was "completely incomprehensible that we had failed to recognise

4085-468: The Born–Oppenheimer approximation. Weaker magnetic dipole and electric quadrupole electronic transitions along with the incomplete validity of the factorization of the total wavefunction into nuclear, electronic spatial and spin wavefunctions means that the selection rules, including the Franck–Condon factor, are not strictly observed. For any given transition, the value of P is determined by all of

4180-587: The Chemistry Division, Franck was also the chairman of the Metallurgical Laboratory's Committee on Political and Social Problems regarding the atomic bomb, which consisted of himself and Donald J. Hughes , J. J. Nickson , Eugene Rabinowitch , Glenn T. Seaborg , J. C. Stearns and Leó Szilárd . In 1945, Franck warned Henry A. Wallace of their fears that "mankind has learned to unleash atomic power without being ethically and politically prepared to use it wisely." The committee compiled what became known as

4275-462: The Faraday Society , James Franck was concerned with the mechanisms of photon-induced chemical reactions. The presumed mechanism was the excitation of a molecule by a photon, followed by a collision with another molecule during the short period of excitation. The question was whether it was possible for a molecule to break into photoproducts in a single step, the absorption of a photon, and without

4370-599: The Hungarian chemist George de Hevesy dissolved the gold medal, along with that of Max von Laue in aqua regia to prevent the Germans from taking them. He placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid. The Nobel Society then recast the Nobel Prize medals. In 1935, Franck moved to

4465-470: The Kaiser Wilhelm Institute examined atomic electrons in their excited state, results that would later prove important in the development of the laser . They coined the term " metastable " for atoms spending an extended time in a state other than that of least energy . When Niels Bohr visited Berlin in 1920, Meitner and Franck arranged for him to come to the Kaiser Wilhelm Institute to talk with

4560-629: The Second Institute for Experimental Physics at the University of Göttingen . While there he worked on quantum physics with Max Born , who was Director of the Institute of Theoretical Physics. His work included the Franck–Hertz experiment , an important confirmation of the Bohr model of the atom . He promoted the careers of women in physics, notably Lise Meitner , Hertha Sponer and Hilde Levi . After

4655-465: The Second Institute for Experimental Physics, a fully tenured professor ordinarius . He was allowed two assistants, so he brought Hertha Sponer with him from Berlin to fill one of the positions. Pohl, a gifted teacher, headed the First Institute, and handled the lectures. Franck refurbished the laboratory with the latest equipment using funds from his own pocket. Under Born and Franck, Göttingen

4750-550: The United States, and he was also able to bring out his elderly mother and aunt. He became a naturalised United States citizen on 21 July 1941, so he was not an enemy alien when the United States declared war on Germany on 11 December 1941. His daughters still were, though, so they were restricted from travelling, and could not take care of their mother when she fell ill and died on 10 January 1942, although they were permitted to attend her funeral. In February 1942, Arthur H. Compton established its Metallurgical Laboratory at

4845-581: The United States, where he had accepted a professorship at Johns Hopkins University. The laboratory there was poorly equipped compared to the one in Göttingen, but he received $ 10,000 for equipment from the Rockefeller Foundation . A more intractable problem was that the university had no money to hire skilled staff. Franck was concerned about his family members remaining in Germany, and needed money to help them emigrate. He therefore accepted an offer from

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4940-530: The University of Chicago. As part of the Manhattan Project , its mission was to build nuclear reactors to create plutonium that would be used in atomic bombs . The Metallurgical Laboratory's Chemistry Division was initially headed by Frank Spedding , but he preferred hands on work to administration. Compton then turned to Franck, with some trepidation owing to his German background. Compton later wrote: How Franck welcomed an invitation to join our project! It

5035-414: The candidate how to conduct original research, while still staying within the limits of the candidate's ability, the laboratory's equipment and the institute's budget. Under his direction, research was carried out into the structure of atoms and molecules. In his own research, Franck developed what became known as the Franck–Condon principle , a rule in spectroscopy and quantum chemistry that explains

5130-438: The chromophores, particularly if the solvent molecules are polar . This association between solvent and solute is referred to as solvation and is a stabilizing interaction, that is, the solvent molecules can move and rotate until the energy of the interaction is minimized. The interaction itself involves electrostatic and van der Waals forces and can also include hydrogen bonds . Franck–Condon principles can be applied when

5225-628: The city of Hamburg awarded him the Hanseatic Cross on 11 January 1916. While in hospital with pleurisy , he co-wrote yet another scientific paper with Hertz, and he was appointed an assistant professor in his absence by Frederick William University on 19 September 1916. Sent to the Russian front , he came down with dysentery . He returned to Berlin, where he joined Hertz, Westphal, Hans Geiger , Otto Hahn and others at Haber's Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry , working on

5320-404: The confining dimension is large compared to the wavelength of the particle. During this state, the bandgap remains at its original energy due to a continuous energy state. However, as the confining dimension decreases and reaches a certain limit, typically in nanoscale, the energy spectrum becomes discrete . As a result, the bandgap becomes size-dependent. As the size of the particles decreases,

5415-559: The density of the mass is so low that tidal forces from other masses are greater than the gravity of the body itself. A potential hill is the opposite of a potential well, and is the region surrounding a local maximum . Quantum confinement can be observed once the diameter of a material is of the same magnitude as the de Broglie wavelength of the electron wave function . When materials are this small, their electronic and optical properties deviate substantially from those of bulk materials. A particle behaves as if it were free when

5510-670: The development of gas masks . He was awarded the Iron Cross, First Class, on 23 February 1918. He was discharged from the Army on 25 November 1918, soon after the war ended. With the war over, Haber's Kaiser Wilhelm Institute now returned to research, and Haber offered Franck a job. His new post came with more pay, but was not a tenured position. It did however allow Franck to pursue his research as he wished. Working with new, younger collaborators such as Walter Grotrian , Paul Knipping, Thea Krüger, Fritz Reiche and Hertha Sponer , his first papers at

5605-427: The electronic transition is essentially instantaneous on the time scale of solvent motion (vertical arrow), the collection of excited state chromophores is immediately far from equilibrium. The rearrangement of the solvent molecules according to the new potential energy curve is represented by the curved arrows in Figure 7. Note that while the electronic transitions are quantized, the chromophore-solvent interaction energy

5700-471: The electronic transitions of chromophores dissolved in liquids. In this use of the Franck–Condon metaphor, the vibrational levels of the chromophores, as well as interactions of the chromophores with phonons in the liquid, continue to contribute to the structure of the absorption and emission spectra, but these effects are considered separately and independently. Consider chromophores surrounded by solvent molecules. These surrounding molecules may interact with

5795-409: The energy of the photon corresponds to the purely electronic transition energy or to the purely electronic transition energy plus the energy of one or more lattice phonons. In the low-temperature approximation, emission is from the zero-phonon level of the excited state to the zero-phonon level of the ground state or to higher phonon levels of the ground state. Just like in the Franck–Condon principle,

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5890-438: The excited state, its interaction with the solvent will be far from equilibrium in the excited state. This effect is analogous to the original Franck–Condon principle: the electronic transition is very fast compared with the motion of nuclei—the rearrangement of solvent molecules in the case of solvation. We now speak of a vertical transition, but now the horizontal coordinate is solvent-solute interaction space. This coordinate axis

5985-466: The expected configuration in space. As a result, surface tension changes tremendously. The Young–Laplace equation can give a background on the investigation of the scale of forces applied to the surface molecules: Under the assumption of spherical shape R 1 = R 2 = R {\displaystyle R_{1}=R_{2}=R} and resolving the Young–Laplace equation for

6080-609: The fundamental significance of Bohr's theory, so much so, that we never even mentioned it once". On 10 December 1926, Franck and Hertz were awarded the 1925 Nobel Prize in Physics "for their discovery of the laws governing the impact of an electron upon an atom.". Franck enlisted in the German Army soon after the outbreak of the First World War in August 1914. In December he was sent to

6175-458: The government. As a veteran of the First World War, Franck was exempt, but he submitted his resignation anyway on 17 April 1933. He once commented that science was his God and nature was his religion. He did not require his daughters to attend religious instruction classes at school, and even let them have a decorated tree at Christmas; but he was proud of his Jewish heritage all the same. He

6270-411: The ground and the first excited state is labeled as q 01 . In the simplest case of a diatomic molecule the nuclear coordinates axis refers to the internuclear separation. The vibronic transition is indicated by a vertical arrow due to the assumption of constant nuclear coordinates during the transition. The probability that the molecule can end up in any particular vibrational level is proportional to

6365-450: The initial vibrational state ( υ ) of the ground electronic level ( ε ), | ϵ v ⟩ {\displaystyle |\epsilon v\rangle } , to some vibrational state ( υ ′) of an excited electronic state ( ε ′), | ϵ ′ v ′ ⟩ {\displaystyle |\epsilon 'v'\rangle } (see bra–ket notation ). The molecular dipole operator μ

6460-453: The intensity of vibronic transitions , simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy. The principle states that during an electronic transition , a change from one vibrational energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly. The principle has since been applied to

6555-400: The interaction energy. The rate of solvent relaxation depends on the viscosity of the solvent. Assuming the solvent relaxation time is short compared with the lifetime of the electronic excited state, emission will be from the lowest solvent energy state of the excited electronic state. For small-molecule solvents such as water or methanol at ambient temperature, solvent relaxation time is on

6650-407: The interactions between the chromophore and the surrounding solvent molecules are different in the ground and in the excited electronic state. This change in interaction can originate, for example, due to different dipole moments in these two states. If the chromophore starts in its ground state and is close to equilibrium with the surrounding solvent molecules and then absorbs a photon that takes it to

6745-416: The low temperature approximation, the molecule starts out in the v = 0 vibrational level of the ground electronic state and upon absorbing a photon of the necessary energy, makes a transition to the excited electronic state. The electron configuration of the new state may result in a shift of the equilibrium position of the nuclei constituting the molecule. In Figure 3 this shift in nuclear coordinates between

6840-467: The molecule do not have time to change during the very brief amount of time involved in an electronic transition. However, this physical intuition can be, and is indeed, routinely extended to interactions between light-absorbing or emitting molecules ( chromophores ) and their environment. Franck–Condon metaphors are appropriate because molecules often interact strongly with surrounding molecules, particularly in liquids and solids, and these interactions modify

6935-404: The new radii R {\displaystyle R} (nm), we estimate the new Δ P {\displaystyle \Delta P} (GPa). The smaller the radii, the greater the pressure is present. The increase in pressure at the nanoscale results in strong forces toward the interior of the particle. Consequently, the molecular structure of the particle appears to be different from

7030-415: The nuclear coordinates of the chromophore in ways closely analogous to the molecular vibrations considered by the Franck–Condon principle. The closest Franck–Condon analogy is due to the interaction of phonons ( quanta of lattice vibrations) with the electronic transitions of chromophores embedded as impurities in the lattice. In this situation, transitions to higher electronic levels can take place when

7125-412: The order of some tens of picoseconds whereas chromophore excited state lifetimes range from a few picoseconds to a few nanoseconds . Immediately after the transition to the ground electronic state, the solvent molecules must also rearrange themselves to accommodate the new electronic configuration of the chromophore. Figure 7 illustrates the Franck–Condon principle applied to solvation. When the solution

7220-528: The overall wavefunctions of the initial and final state. The overall wavefunctions are the product of the individual vibrational (depending on spatial coordinates of the nuclei) and electronic space and spin wavefunctions: This separation of the electronic and vibrational wavefunctions is an expression of the Born–Oppenheimer approximation and is the fundamental assumption of the Franck–Condon principle. Combining these equations leads to an expression for

7315-408: The positions of the nuclei in the molecular entity and its environment. The resulting state is called a Franck–Condon state, and the transition involved, a vertical transition. The quantum mechanical formulation of this principle is that the intensity of a vibronic transition is proportional to the square of the overlap integral between the vibrational wavefunctions of the two states that are involved in

7410-415: The possible combinations of allowed and forbidden spin and orbital selection rules. The Franck–Condon principle, in its canonical form, applies only to changes in the vibrational levels of a molecule in the course of a change in electronic levels by either absorption or emission of a photon. The physical intuition of this principle is anchored by the idea that the nuclear coordinates of the atoms constituting

7505-528: The probability amplitude in terms of separate electronic space, spin and vibrational contributions: The spin-independent part of the initial integral is here approximated as a product of two integrals: This factorization would be exact if the integral ∫ ψ e ′ ∗ μ e ψ e d τ e {\displaystyle \int \psi _{e}'^{*}{\boldsymbol {\mu }}_{e}\psi _{e}\,d\tau _{e}} over

7600-443: The probability of transitions involving phonons is determined by the overlap of the phonon wavefunctions at the initial and final energy levels. For the Franck–Condon principle applied to phonon transitions, the label of the horizontal axis of Figure 1 is replaced in Figure 6 with the configurational coordinate for a normal mode . The lattice mode q i {\displaystyle q_{i}} potential energy in Figure 6

7695-403: The selection rules, however spin selection is the largest contributor, followed by electronic selection rules. The Franck–Condon factor only weakly modulates the intensity of transitions, i.e., it contributes with a factor on the order of 1 to the intensity of bands whose order of magnitude is determined by the other selection rules. The table below gives the range of extinction coefficients for

7790-417: The spatial coordinates of the electrons would not depend on the nuclear coordinates. However, in the Born–Oppenheimer approximation ψ e {\displaystyle \psi _{e}} and ψ e ′ {\displaystyle \psi '_{e}} do depend (parametrically) on the nuclear coordinates, so that the integral (a so-called transition dipole surface )

7885-406: The square of the (vertical) overlap of the vibrational wavefunctions of the original and final state (see Quantum mechanical formulation section below). In the electronic excited state molecules quickly relax to the lowest vibrational level of the lowest electronic excitation state ( Kasha's rule ), and from there can decay to the electronic ground state via photon emission. The Franck–Condon principle

7980-472: The states. Shown in the diagram is the change in electron energy level and bandgap between nanomaterial and its bulk state. The following equation shows the relationship between energy level and dimension spacing: Research results provide an alternative explanation of the shift of properties at nanoscale. In the bulk phase, the surfaces appear to control some of the macroscopically observed properties. However, in nanoparticles , surface molecules do not obey

8075-569: The subject, which he would return to over the following years. Franck found a position at the Polytekniske Læreanstalt in Copenhagen for Arthur von Hippel, who was now his son in law, having married his daughter Dagmar. He decided to provide financial security for his children by dividing his Nobel Prize money between them. The gold medal itself was entrusted to Niels Bohr for safekeeping. When Germany invaded Denmark on 9 April 1940,

8170-411: The theory is the behaviour of the exciton resembles that of an atom as its surrounding space shortens. A rather good approximation of an exciton's behaviour is the 3-D model of a particle in a box . The solution of this problem provides a sole mathematical connection between energy states and the dimension of space. Decreasing the volume or the dimensions of the available space, increases the energy of

8265-487: The transition. In the quantum mechanical picture, the vibrational levels and vibrational wavefunctions are those of quantum harmonic oscillators , or of more complex approximations to the potential energy of molecules, such as the Morse potential . Figure 1 illustrates the Franck–Condon principle for vibronic transitions in a molecule with Morse-like potential energy functions in both the ground and excited electronic states. In

8360-575: The younger staff without the presence of the bonzen ("bigwigs"). In 1920, the University of Göttingen offered Max Born its chair of theoretical physics, which had recently been vacated by Peter Debye . Göttingen was an important centre for mathematics, thanks to David Hilbert , Felix Klein , Hermann Minkowski and Carl Runge , but not so much for physics. This would change. As part of his price for coming to Göttingen, Born wanted Franck to head experimental physics there. On 15 November 1920, Franck became Professor of Experimental Physics and Director of

8455-545: Was a vote of confidence that far exceeded his hopes, and it gave him a chance to do his part for the cause of freedom. "It's not the German people I'm fighting", he explained. "It's the Nazis. They have a stranglehold over Germany. The German people are helpless until we can break the strength of their Nazi masters." The chemists welcomed Franck as an elder scientific statesman whose guidance they were glad to follow. In addition to heading

8550-624: Was also an International Member of the American Philosophical Society . He died suddenly from a heart attack while visiting Göttingen on 21 May 1964, and was buried in Chicago with his first wife. In 1967, the University of Chicago named the James Franck Institute after him. A lunar crater has also been named in his honour. His papers are in the University of Chicago Library. Potential well A potential well

8645-780: Was awarded the Max Planck medal of the Deutsche Physikalische Gesellschaft in 1951 and the Rumford Medal of the American Academy of Arts and Sciences for his work on photosynthesis in 1955. He became an honorary citizen of Göttingen in 1953, was elected a member of the United States National Academy of Sciences in 1944, and elected a Foreign Member of the Royal Society (ForMemRS) in 1964 . He

8740-530: Was far more interested in those on science. While there, he met Max Born , who would become a lifelong friend. With Born's help, he was able to persuade his parents to allow him to switch to studying physics and chemistry. Franck attended mathematics lectures by Leo Königsberger and Georg Cantor , but Heidelberg was not strong on the physical sciences, so he decided to go to the Frederick William University in Berlin. At Berlin, Franck attended lectures by Max Planck and Emil Warburg . On 28 July 1904 he saved

8835-596: Was one of the world's great centres for physics between 1920 and 1933. Although they published only three papers together, Born and Franck discussed every one of their papers with each other. Gaining admittance to Franck's laboratory became highly competitive. His doctoral students included Hans Kopfermann , Arthur R. von Hippel , Wilhelm Hanle , Fritz Houtermans , Heinrich Kuhn , Werner Kroebel  [ de ] , Walter Lochte-Holtgreven and Heinz Maier-Leibnitz . In supervising doctoral candidates, Franck had to ensure that thesis topics were well-defined, and would teach

8930-438: Was the first academic to resign in protest over the law. Newspapers around the world reported it, but no government or university protested. Franck assisted Frederick Lindemann in helping dismissed Jewish scientists find work overseas, before he left Germany in November 1933. After a brief visit to the United States, where he measured the absorption of light in heavy water with Wood at Johns Hopkins University , he took up

9025-400: Was with Gustav Hertz , with whom he wrote 19 articles. He received his habilitation on 20 May 1911. In 1914, Franck teamed up with Hertz to perform an experiment to investigate fluorescence . They designed a vacuum tube for studying energetic electrons that flew through a thin vapour of mercury atoms. They discovered that when an electron collided with a mercury atom it could lose only

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