#### Answer

a. 300 nm. b. 200 nm.

#### Work Step by Step

a. We are told that the B-to-A transition has twice the energy of the C-to-B transition. Therefore the emitted photon will have twice the frequency and half the wavelength. $(\frac{1}{2})(600 nm) = 300 nm$.
For photons, E = hf, where E is the energy, h is Planck's constant, and f is the photon's vibrational frequency. A high frequency means high energy per photon. This is discussed on page 564.
From our study of wave motion, page 362, we also know that $\lambda = \frac{c}{f}$, where c is the speed of light. The photon wavelength is inversely proportional to its frequency.
In summary, twice the energy means twice the frequency, which means half the wavelength.
b. We can deduce that the C-to-A transition has three times the energy of the C-to-B transition. Therefore the emitted photon will have three times the frequency and one-third the wavelength. $(\frac{1}{3})(600 nm) = 200 nm$.
For photons, E = hf, where E is the energy, h is Planck's constant, and f is the photon's vibrational frequency. A high frequency means high energy per photon. This is discussed on page 564.
From our study of wave motion, page 362, we also know that $\lambda = \frac{c}{f}$, where c is the speed of light. The photon wavelength is inversely proportional to its frequency.
In summary, three times the energy means thrice the frequency, which means one-third the wavelength.