An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 W. An infrared lamp emits light of wave- length 700 nm, also at the rate of 400 W. (a) Which lamp emits photons at the greater rate and (b) what is that greater rate?

Explanation

To solve the problem, we need to find out which lamp emits photons at a greater rate and calculate that rate.

### Step-by-Step Solution:

1. **Understand the relationship between power, energy of a photon, and rate of photon emission:**
The power (P) emitted by a lamp is related to the rate of photon emission (R) and the energy of each photon (E) by the equation:
\[
P = R \cdot E
...