A 75 W light source emits light of wavelength 600 nm. (a) Calculate the frequency of the emitted light.
(b) How many photons per second does the source emit?

Explanation

To solve the given problem step by step, we will break it down into two parts as specified in the question.

### Part (a): Calculate the frequency of the emitted light.

1. **Identify the known values:**
- Power of the light source, \( P = 75 \, \text{W} \)
- Wavelength of the light, \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
- Speed of light, \( c = 3 \times 10^8 \, \text{m/s} \)

2. **Use the formula to calculate frequency:**
\[ f = \frac{c}{\lambda} \]

3. **Substitute the values into the formula:**
\[ f = \frac{3 \times 10^8 \, \text{m/s}}{600 \times 10^{-9} \, \text{m}} \]

4. **Calculate the frequency:**
\[ f = \frac{3 \times 10^8}{600 \times 10^{-9}} = \frac{3 \times 10^8}{6 \times 10^{-7}} = \frac{3}{6} \times 10^{8 + 7} = 0.5 \times 10^{15} = 5 \times 10^{14} \, \text{Hz} \]

5. **Final answer for frequency:**
\[ f = 5 \times 10^{14} \, \text{Hz} \]

### Part (b): How many photons per second does the source emit?

1. **Calculate the energy of a single photon using the frequency:**
\[ E = h \cdot f \]
where \( h \) (Planck's constant) is \( 6.626 \times 10^{-34} \, \text{J s} \).

2. **Substitute the frequency into the energy formula:**
\[ E = 6.626 \times 10^{-34} \, \text{J s} \cdot 5 \times 10^{14} \, \text{Hz} \]

3. **Calculate the energy of one photon:**
\[ E = 6.626 \times 5 \times 10^{-34} \times 10^{14} = 33.13 \times 10^{-20} = 3.313 \times 10^{-19} \, \text{J} \]

4. **Calculate the number of photons emitted per second:**
\[ n_p = \frac{P}{E} \]
where \( P = 75 \, \text{W} = 75 \, \text{J/s} \).

5. **Substitute the values:**
\[ n_p = \frac{75 \, \text{J/s}}{3.313 \times 10^{-19} \, \text{J}} \]

6. **Calculate the number of photons:**
\[ n_p \approx 2.26 \times 10^{20} \, \text{photons/s} \]

7. **Final answer for the number of photons emitted per second:**
\[ n_p \approx 2.26 \times 10^{20} \, \text{photons/s} \]

### Summary of Answers:
- (a) Frequency of the emitted light: \( f = 5 \times 10^{14} \, \text{Hz} \)
- (b) Number of photons emitted per second: \( n_p \approx 2.26 \times 10^{20} \, \text{photons/s} \)