PHYS 3310 Module 9 Self Assessment Practice Problems

Module 9 Self Assessment Practice Problems

9.1
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

9.2
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

9.3
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

9.4
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

9.5
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

9.6
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

9.7
Compute the K_α X ray energies of calcium (Z = 20), zirconium (Z = 40), and mercury (Z = 80). Compare with the measured values of 3.69 keV, 15.8 keV, and 70.8 keV.
Answer: 3.68 keV, 15.5 keV, 63.7 keV

9.8
A small helium–neon laser produces a light beam with an average power of 3.5 mW and a diameter of 2.4 mm.
(a) How many photons per second are emitted by the laser?
(b) What is the amplitude of the electric field of the light wave? Compare this result with the electric field at a distance of 1 m from an incandescent light bulb that emits 100 W of visible light.
Answer: (a) 1.1 x 10¹⁶ photons/s (b) 764 V/m, 77.4 V/m

9.9
A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 𝜇m. In 1.00 ms, this laser raised the temperature of 1.00 cm³ of flesh to 100°C and evaporated it.
(a) How many photons were required? You may assume that flesh has the same heat of vaporization as water.
(b) What was the minimum power output during the flash?
Answer: (a) 1.21 x 10²³ photons (b) 2.3 MW

9.10
The red light emitted by a ruby laser has a wavelength of 694.3 nm. What is the difference in energy between the initial state and final state corresponding to the emission of the light?
Answer: 1.79 eV