Using a mixture of CO₂, N₂, and sometimes He, CO₂ lasers emit a wavelength of $10.6$ $\mu$m. At power of $0.100$ kW, such lasers are used for surgery. How many photons per second does a CO₂ laser deliver to the tissue during its use in an operation?

Two stars, both of which behave like ideal blackbodies, radiate the same total energy per second. The cooler one has a surface temperature $T$ and a diameter $3.0$ times that of the hotter star.

(a) What is the temperature of the hotter star in terms of $T$?

(b) What is the ratio of the peak-intensity wavelength of the hot star to the peak-intensity wavelength of the cool star?

The shortest visible wavelength is about $400$ nm. What is the temperature of an ideal radiator whose spectral emittance peaks at this wavelength?

Photorefractive keratectomy (PRK) is a laser-based surgical procedure that corrects near- and farsightedness by removing part of the lens of the eye to change its curvature and hence focal length. This procedure can remove layers $0.25$ mm thick using pulses lasting $12.0$ ns from a laser beam of wavelength $193$ nm. Low-intensity beams can be used because each individual photon has enough energy to break the covalent bonds of the tissue. If a $1.50$-mW beam is used, how many photons are delivered to the lens in each pulse?

How many photons per second are emitted by a $7.50$-mW CO₂ laser that has a wavelength of $10.6$ mm?

Use Balmer's formula to calculate (a) the wavelength, (b) the frequency, and (c) the photon energy for the Hg line of the Balmer series for hydrogen.

Find the longest and shortest wavelengths in the Lyman and Paschen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?

A triply ionized beryllium ion, Be³⁺ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. For the hydrogen atom, the wavelength of the photon emitted in the $n=2$ to $n=1$ transition is $122$ nm (see Example $39.6$). What is the wavelength of the photon emitted when a Be³⁺ ion undergoes this transition?

A triply ionized beryllium ion, Be³⁺ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. What is the ground-level energy of Be³⁺? How does this compare to the ground-level energy of the hydrogen atom?