A laser emits a single, 2.0 ms pulse of light that has a frequency of `2.83 xx 10^(11) Hz` and a total power of 75 000 W. How many photons are in the pulse?

Options

A. `8.0 xx 10^(23)`
B. `2.4 xx 10^(25)`
C. `1.6 xx 10^(24)`
D. `3.2 xx 10^(25)`

Answer

To determine the number of photons emitted in a pulse of light from a laser, we can follow these steps:

### Step 1: Calculate the total energy emitted by the laser
The total energy (E) emitted by the laser can be calculated using the formula:
\[ E = P \times t \]
where:
- \( P \) is the power of the laser (in watts),
- \( t \) is the time duration of the pulse (in seconds).

Given:
- \( P = 75,000 \, \text{W} \)
- \( t = 2.0 \, \text{ms} = 2.0 \times 10^{-3} \, \text{s} \)

Substituting the values:
\[ E = 75,000 \, \text{W} \times 2.0 \times 10^{-3} \, \text{s} = 150 \, \text{J} \]

### Step 2: Calculate the energy of a single photon
The energy (E_photon) of a single photon can be calculated using the formula:
\[ E_{\text{photon}} = h \times \nu \]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( \nu \) is the frequency of the light (in Hz).

Given:
- \( \nu = 2.83 \times 10^{11} \, \text{Hz} \)

Substituting the values:
\[ E_{\text{photon}} = 6.626 \times 10^{-34} \, \text{J s} \times 2.83 \times 10^{11} \, \text{Hz} \]
\[ E_{\text{photon}} \approx 1.877 \times 10^{-22} \, \text{J} \]

### Step 3: Calculate the number of photons emitted
The number of photons (n) emitted can be calculated using the formula:
\[ n = \frac{E}{E_{\text{photon}}} \]

Substituting the values:
\[ n = \frac{150 \, \text{J}}{1.877 \times 10^{-22} \, \text{J}} \]
\[ n \approx 8.0 \times 10^{23} \]

### Conclusion
The number of photons in the pulse is approximately \( 8.0 \times 10^{23} \).

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