A laser emits a pulse of light with energy `5.0 xx 10^(3)J`. Determine the number of photons in the pulse if the wavelength of light is 480 nm.

Options

A. `5.2 xx 10^(16)`
B. `1.2 xx 10^(22)`
C. `2.5 xx 10^(19)`
D. `3.1 xx 10^(22)`

Answer

To determine the number of photons in a laser pulse with a given energy and wavelength, we can follow these steps:

### Step 1: Understand the relationship between energy, wavelength, and photons
The energy of a single photon can be calculated using the formula:
\[ E_{\text{photon}} = \frac{hc}{\lambda} \]
where:
- \(E_{\text{photon}}\) is the energy of one photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength of the light in meters.

### Step 2: Convert the wavelength from nanometers to meters
Given the wavelength \(\lambda = 480 \, \text{nm}\):
\[ \lambda = 480 \, \text{nm} = 480 \times 10^{-9} \, \text{m} \]

### Step 3: Calculate the energy of a single photon
Substituting the values into the photon energy formula:
\[ E_{\text{photon}} = \frac{(6.626 \times 10^{-34} \, \text{J s})(3.00 \times 10^8 \, \text{m/s})}{480 \times 10^{-9} \, \text{m}} \]

Calculating the numerator:
\[ hc = 6.626 \times 10^{-34} \times 3.00 \times 10^8 = 1.9878 \times 10^{-25} \, \text{J m} \]

Now, calculate \(E_{\text{photon}}\):
\[ E_{\text{photon}} = \frac{1.9878 \times 10^{-25}}{480 \times 10^{-9}} = 4.13875 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the total number of photons
The total energy of the pulse is given as \(5.0 \times 10^3 \, \text{J}\). The number of photons \(n\) can be calculated using:
\[ n = \frac{E_{\text{total}}}{E_{\text{photon}}} \]
Substituting the values:
\[ n = \frac{5.0 \times 10^3}{4.13875 \times 10^{-19}} \]

Calculating \(n\):
\[ n \approx 1.21 \times 10^{22} \]

### Conclusion
The number of photons in the pulse is approximately:
\[ n \approx 1.21 \times 10^{22} \]

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