PHYS 3330 Module 2 Self Assessment Practice Problems

Module 2 Self Assessment Practice Problems

2.1
(a) When a hydrogen atom is in its ground state, what are the shortest and longest wavelengths of the photons it can absorb without being ionized?
(b) When a hydrogen atom is in its third excited state, what are the shortest and longest wavelengths of the photons it can emit?
(c) What is the longest wavelength that light can have if it is to be capable of ionizing the hydrogen atom in its ground state?
Answer: (a) 91 nm, 121.6 nm (b) 97.3 nm, 1879 nm (c) 91 nm

2.2
A 4.653-μm emission line of atomic hydrogen corresponds to transition between the states 𝑛_𝑓 = 5 and 𝑛_𝑖. Find 𝑛_𝑖.
Answer: 7

2.3
Calculate the frequency, energy (in keV), and wavelength of the K_α x ray for the elements:
(a) calcium (Ca, Z = 20)
(b) cobalt (Co, Z = 27)
(c) cadmium (Cd, Z = 48)
Answer: (a) 8.9 x 10¹⁷ Hz, 0.337 nm (b) 1.7 x 10¹⁸ Hz, 0.18 nm (c) 5.45 x 10¹⁸ Hz, 0.055 nm

2.4
A K_α x ray emitted from a sample has an energy of 7.46 keV. Of which element is the sample made?
Answer: Ni

2.5
What is the minimum frequency of a photon required to ionize:
(a) a He⁺ ion in its ground state?
(b) A Li²⁺ ion in its first excited state?
Answer: (a) 1.32 x 10¹⁶ Hz (b) 7.4 x 10¹⁵ Hz

2.6
The ion Li²⁺ makes an atomic transition from an n = 4 state to an n = 2 state.
(a) What is the energy of the photon emitted during the transition?
(b) What is the wavelength of the photon?
Answer: (a) 22.95 eV (b) 54 nm

2.7
What is the kinetic energy of an Auger electron released from the L shell of gold (binding energy of L-shell electrons is 13.335 keV) as an electron falls from the L to the K shell (binding energy of K-shell electrons is 80.713 keV)?
Answer: 54.043 keV

2.8
Calculate the energy required for the transition of an electron from the K shell to the L shell in tungsten. Compare the result with the energy necessary for a similar transition in hydrogen. Explain the difference.
Answer: 57.4 keV, compared to 10.2 eV

2.9
X-rays are produced by striking a target with a beam of electrons. Prior to striking the target, the electrons are accelerated by an electric field through a potential energy difference: ΔU = -eΔV, where e is the charge of an electron and ΔV is the voltage difference.
(a) If ΔV = 15,000 volts, what is the minimum wavelength of the emitted radiation?
(b) What happens to the minimum wavelength if the voltage across the X-ray tube is doubled?
Answer: (a) 82.7 pm (b) it is halved

2.10
The maximum characteristic X-ray photon energy comes from the capture of a free electron into a K shell vacancy. What is this photon energy in keV for tungsten, assuming that the free electron has no initial kinetic energy?
Answer: 72.5 keV