Still have a few registered iclickers (3 or 4 Still have a few registered iclickers (3 or 4 ?) that need to be mapped to names

Review: The Bohr model of hydrogen (Bohr radius) Here n is the “principal quantum number” and a0 is the “Bohr radius”, which is the minimum radius of an electron orbital.

Review: The Bohr model of hydrogen (Energy levels) Note that E and U are negative (1/8-1/4=-1/8) This expression for the allowed energies can be rewritten and used to predict atomic spectral lines !

Review: The Bohr model of hydrogen (Energy levels) Here R is the “Rydberg constant”, R=1.097 x 107 m-1 Also hcR = 13.60 eV is a useful result. Question: How can we find the energies of photon transitions between atomic levels ?

Review and Practice: The Bohr model of hydrogen (Clicker questions) Also good preparation for the second problem on the midterm Next topics: the Laser, Blackbody Radiation and Heisenberg’s uncertainty principle revisted.

A certain atom has two energy levels whose energies differ by 2.5 eV. Bohr model A certain atom has two energy levels whose energies differ by 2.5 eV. In order for a photon to excite an electron from the lower energy level to the upper energy level, what must be true about the energy of the photon? A. Its energy must be greater than or equal to 2.5 eV. B. Its energy must be exactly 2.5 eV. C. Its energy must be less than or equal to 2.5 eV. D. none of the above Answer: B

Bohr model A certain atom has two energy levels whose energies differ by 2.5 eV. In order for a photon to excite an electron from the lower energy level to the upper energy level, what must be true about the energy of the photon? A. Its energy must be greater than or equal to 2.5 eV. B. Its energy must be exactly 2.5 eV. C. Its energy must be less than or equal to 2.5 eV. D. none of the above

Bohr model II A certain atom has only three energy levels. From lowest to highest energy, these levels are denoted n = 1, n = 2, and n = 3. When the atom transitions from the n = 3 level to the n = 2 level, it emits a photon of wavelength 800 nm. When the atom transitions from the n = 2 level to the n = 1 level, it emits a photon of wavelength 200 nm. What is the wavelength of the photon emitted when the atom transitions from the n = 3 level to the n = 1 level? 1000 nm 600 nm C. 500 nm D. 160 nm Answer: D

Bohr model II A certain atom has only three energy levels. From lowest to highest energy, these levels are denoted n = 1, n = 2, and n = 3. When the atom transitions from the n = 3 level to the n = 2 level, it emits a photon of wavelength 800 nm. When the atom transitions from the n = 2 level to the n = 1 level, it emits a photon of wavelength 200 nm. What is the wavelength of the photon emitted when the atom transitions from the n = 3 level to the n = 1 level? 1000 nm 600 nm C. 500 nm D. 160 nm 1/lambda = R(1/n_L^2 -1/n_U^2) R (1/3^2 – 1/2^2) = R(1/9-1/4) = 800nm R(1/9-1) = ? 1/800nm = R(1/4-1/9)=R(0.138) ; 1/200 nm = R (1-1/4)=R(0.75) 1/? = R(1-1/9)=R(0.89)

Bohr model III In the Bohr model of the hydrogen atom, an electron in the n = 2 orbit has A. a higher total energy and a higher kinetic energy than an electron in the n =1 orbit. B. a lower total energy and a higher kinetic energy than an electron in the n =1 orbit. C. a higher total energy and a lower kinetic energy than an electron in the n =1 orbit. D. a lower total energy and a lower kinetic energy than an electron in the n =1 orbit. E. none of the above Answer: C

Bohr model III In the Bohr model of the hydrogen atom, an electron in the n = 2 orbit has A. a higher total energy and a higher kinetic energy than an electron in the n =1 orbit. B. a lower total energy and a higher kinetic energy than an electron in the n =1 orbit. C. a higher total energy and a lower kinetic energy than an electron in the n =1 orbit. (Note that E is less negative and goes like 1/n2, while K is positive and goes like 1/n2) D. a lower total energy and a lower kinetic energy than an electron in the n =1 orbit. E. none of the above negative Note that E is less negative

Application of the Bohr model In an alkali “Rydberg atom” the principal quantum number may reach n=1000. Question: How big is a Rydberg atom ?

Small correction to the Bohr model The proton is not infinitely heavy (only ~1836 x the proton mass) and hence the proton and electron revolve around their common center of mass in the Bohr model. For deuterium, m nucleus=m(proton) + m(neutron) mreduced=0.99973m, which is detectable. Used by Harold Urey to discover deuterium (1934 Nobel Prize in Chemistry).

The laser Atoms spontaneously emit photons of frequency f when they transition from an excited energy level to a lower level. Excited atoms can be stimulated to emit coherently if they are illuminated with light of the same frequency f. This happens in a laser (Light Amplification by Stimulated Emission of Radiation) discovered by A. Einstein in 1916 (one γ in two γ’s out)

The laser Need a “population inversion” in state E2, which is relatively long-lived (10-3s) compared to E3 or E1 (10-8s). Stimulated emission from E2 to E1 Note that the mirrors and resonant cavity are needed.

Conceptual question on lasers An ordinary neon light fixture like those used in advertising signs emit red light of wavelength 632.8 nm. Neon is also used in a helium-neon laser (HeNe). The light emitted by a neon light fixture is an example of Spontaneous emission Stimulated emission Both Spontaneous and stimulated emission. Ans: A (potential difference is applied across the tube to excite Ne atoms into an excited state). However, there is no population inversion or resonant cavity etc.

Continuous spectra and blackbody radiation A blackbody is an idealized case of a hot, dense object. The continuous spectrum produced by a blackbody at different temperatures is shown on the right (the sun is another example) Note: Usually a heated solid or liquid produces a continuous blackbody frequency spectrum

Continuous spectra and blackbody radiation Stefan-Boltzmann Law for blackbody radiation (PHYS170); Here σ is the Stefan-Boltzmann constant. The surface of the Sun with a sunspot. T(sunspot)=4000K, T(sun)=5800 K; ratio of I’s is (4000/5800)4 =0.23dark Questions: What are the units of intensity ? This is the Wien displacement law (PHYS170). where λm is the peak wavelength and T is the temperature