Problems from "The MCAT Physics Book" A hydrogen atom has energy levels given by En--(13.6 ev)- where n is a positive integer. A state in which the electron is infinitely far from the nucleus corresponds to 0 ev. (Note: 1 ev = 1.602 x 10" J) The energy level diagram is shown in the figure below. An atom generally has an electron in a given energy level; however, a transition may occur if the atom absorbs or emits a photon, or particle of light. 0 ev -0.8 ev -1.5 ev -3.4 ev E -13.6 ev For the following questions, consider a hydrogen atom in an excited state initially at rest. It emits a photon of energy E, which travels to the right. The hydrogen atom is now in its ground state. The energy of a photon is given by Ephoton = hf, where fis the frequency and h = 4.14 x 10-15 ev s. The momentum of a photon is given by Pphoton = Elc, where c = 3.0 x 10 m/s, the speed of light. The mass of a hydrogen atom is m₁ = 1.7 x 10 27 kg. 1. What is the smallest energy a photon must have to boost a hydrogen atom in its ground state to an excited state? A.3.4 ev B. 10.2 ev C. 13.6 ev D. There is no smallest energy. 2. What is the ionization energy for a hydrogen atom? A. 1.5 ev B.3.4 ev C. 10.2 ev D. 13.6 ev 3. A hydrogen atom in its ground state absorbs a photon and ends up in the excited state corresponding to 3. What is the most restrictive statement that can be concluded about the photon? A. The photon had an energy of 12.1 ev. B. The photon had an energy greater than or equal to 12.1 ev. C. The photon had an energy greater than 12.1 ev but less than 12.8 ev. D. The photon had an energy greater than 10.2 ev. 4. In the scenario mentioned in the second paragraph, what can be concluded? A. Momentum is conserved, but not energy. B. Energy is conserved, but not momentum. C. Both momentum and energy are conserved. D. Neither momentum nor energy is conserved, 5. What is the longest wavelength CS Scanned with CamScanner corresponding to a photon which could cause a transition in a hydrogen atom? A. 9.1 x 10% m B. 1.2 x 107 m C. 3.6 x 107 m D. There is no longest wavelength. 11. If an atom has only the three energy levels shown in the figure below, what possible frequencies might be in the spectrum of this atom? (Use h = 4.14 x 10-15 ev s and c = 3.0 x 108 m/s.) 4 ev Et I ev 0 ev 14. The figure below shows the known energy level diagram for a hypothetical atom. A brilliant young scientist discovers a new spectral line with frequency 4.8 x 10 Hz. which she determines is a transition from the ground state to an excited state. What is the energy of the (excited) quantum state she has discovered? (Use h = 4.14 x 10-15 ev s and c=3.0 x 108 m/s.) A. 7.2 x 1014 Hz B. 2.4 x 104 Hz and 7.2 x 1014 Hz C. 2.4 x 104 Hz and 9.7 x 1014 Hz D. 2.4 x 104 Hz, 7.2 x 1014 Hz, and 9.7 x 1014 Hz A.-7 ev B. 4 ev C.-3 ev D.-2 ev E↑ 0 ev -1.5 ev -5 ev The figure below shows the energy level diagram of a hypothetical atom. Light in the visible portion of the spectrum has frequency between 4.0 x 10 Hz and 7.5 x 104 Hz. (Use h = 4.14 x 10-15 ev s and c = 3.0 x 108 m/s.) 0 ev -1 ev -2.5 ev E↑ -6 ev 12. What is the maximum number of spectral lines for this atom? A. 1 B. 3 C.4 D.6 13. How many lines are possible in the visible spectrum? A.0 B. 1 C.2 D. 3 Atoms of lithium are able to absorb photons of frequency 2.01 x 1014 Hz. This corresponds to a transition from the ground state (at -5.37 ev) to an excited state. Zero energy corresponds to the state in which one electron is completely removed from the atom. (Use h = 4.14 x 10-15 ev s and c = 3.0 x 108 m/s.) 15. What is the energy of the excited state referred to in the passage? A.-6.20 ev B.-4.54 ev C.-0.83 ev D. 6.20 ev 16. What is the wavelength of light corresponding to this transition? A.2.3 x 10-7 m B. 1.5 x 10-6 m C. 4.3 x 10 m D. 6.7 x 105 m 17. If a photon ionizes a lithium atom, what conclusion can be drawn about the photon? A. It had frequency less than 1.3 x 1015 Hz. B. It had frequency 1.3 x 1015 Hz. C. It had frequency greater than 1.3 x 1015 Hz. D. None of the above may be concluded. CS Scanned with CamScanner