8.6 Lasers

Why is a metastable state necessary for the production of laser light?

How is a Blu-Ray player able to read more information that a CD player?

A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of $10.6 \mu \text{m}$. In 1.00 ms, this laser raised the temperature of $1.00 \text{cm}^{3}$ of flesh to $100 °\text{C}$ 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?

For a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is $\theta = \text{cos}^{−1} \left(\sqrt{\frac{n - 1}{n}}\right) .$

Sketch the potential energy function of an electron in a hydrogen atom. (a) What is the value of this function at $r = 0$? in the limit that $r = \infty$? (b) What is unreasonable or inconsistent with the former result?

Show that the maximum number of orbital angular momentum electron states in the nth shell of an atom is $n^{2}$. (Ignore electron spin.) (Hint: Make a table of the total number of orbital angular momentum states for each shell and find the pattern.)

What is the maximum number of electron states in the $n = 5$ shell?

Show that the maximum number of electron states in the nth shell of an atom is $2 n^{2}$.

Which of the following notations are allowed (that is, which violate none of the rules regarding values of quantum numbers)? (a) $1 s^{1} ;$ (b) $1 d^{3} ;$ (c) $4 s^{2} ;$ (d) $3 p^{7} ;$ (e) $6 h^{20}$

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

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

A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, they observe a yellow line and find its wavelength to be 589 nm. (a) Assuming that this is part of the Balmer series, determine $n_{\text{i}} ,$ the principal quantum number of the initial state. (b) What is unreasonable about this resul…