8.6 Lasers  (Page 3/9)

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

How does light from an incandescent light bulb differ from laser light?

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

What are the similarities and differences between a CD player and a Blu-Ray 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?

An excimer laser used for vision correction emits UV radiation with a wavelength of 193 nm. (a) Calculate the photon energy in eV. (b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. That is, divide the heat of vaporization in kJ/kg by the number of water molecules in a kilogram. (c) Convert this to eV and compare to the photon energy. Discuss the implications.

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 $\theta ={\text{cos}}^{\mathrm{-1}}\left(\sqrt{\frac{n-1}{n}}\right).$

What is the probability that the 1 s electron of a hydrogen atom is found between $r=0$ and $r=\infty ?$

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?

Find the value of $l$ , the orbital angular momentum quantum number, for the Moon around Earth.

Show that the maximum number of orbital angular momentum electron states in the n th 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 magnitude of an electron magnetic moment?

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

A ground-state hydrogen atom is placed in a uniform magnetic field, and a photon is emitted in the transition from a spin-up to spin-down state. The wavelength of the photon is $168\mu \text{m}$ . What is the strength of the magnetic field?

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

The valence electron of chlorine is excited to a 3 p state. (a) What is the magnitude of the electron’s orbital angular momentum? (b) What are possible values for the z -component of angular measurement?

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

The ion ${\text{Be}}^{\text{3+}}$ makes an atomic transition from an $n=3$ 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 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?

Derive an expression for the ratio of X-ray photon frequency for two elements with atomic numbers $Z_1$ and $Z_2.$

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

(a) What voltage must be applied to an X-ray tube to obtain 0.0100-fm-wavelength X-rays for use in exploring the details of nuclei? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

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, she observes a yellow line and finds 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 result? (c) Which assumptions are unreasonable or inconsistent?