8.5 Atomic spectra and x-rays  (Page 7/12)

The ion ${\text{Li}}^{\text{2+}}$ 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?

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?

The yellow light from a sodium-vapor street lamp is produced by a transition of sodium atoms from a 3 p state to a 3s state. If the difference in energies of those two states is 2.10 eV, what is the wavelength of the yellow light?

Estimate the wavelength of the $K_{\text{α}}$ X-ray from calcium.

Estimate the frequency of the $K_{\text{α}}$ X-ray from cesium.

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:

$\text{Δ}U=\text{−}e\text{Δ}V,$

where e is the charge of an electron and $\text{Δ}V$ is the voltage difference. If $\text{Δ}V=\mathrm{15,000}$ volts, what is the minimum wavelength of the emitted radiation?

For the preceding problem, what happens to the minimum wavelength if the voltage across the X-ray tube is doubled?

Suppose the experiment in the preceding problem is conducted with muons. What happens to the minimum wavelength?

An X-ray tube accelerates an electron with an applied voltage of 50 kV toward a metal target. (a) What is the shortest-wavelength X-ray radiation generated at the target? (b) Calculate the photon energy in eV. (c) Explain the relationship of the photon energy to the applied voltage.

A color television tube generates some X-rays when its electron beam strikes the screen. What is the shortest wavelength of these X-rays, if a 30.0-kV potential is used to accelerate the electrons? (Note that TVs have shielding to prevent these X-rays from exposing viewers.)

An X-ray tube has an applied voltage of 100 kV. (a) What is the most energetic X-ray photon it can produce? Express your answer in electron volts and joules. (b) Find the wavelength of such an X-ray.

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?

What are the approximate energies of the $K_{\alpha }$ and $K_{\beta }$ X-rays for copper?

Compare the X-ray photon wavelengths for copper and gold.

The approximate energies of the $K_{\alpha }$ and $K_{\beta }$ X-rays for copper are $E_{K_{\alpha }}=8.00\text{keV}$ and $E_{K_{\beta }}=9.48\text{keV,}$ respectively. Determine the ratio of X-ray frequencies of gold to copper, then use this value to estimate the corresponding energies of $K_{\alpha }$ and $K_{\beta }$ X-rays for gold.