How many photons are emitted per second by a 5 mW laser source operating at 632.8 nm?

Options

A. `1.6xx10^(16)`
B. `1.6xx10^(13)`
C. `1.6xx10^(10)`
D. `1.6xx10^(3)`

Explanation

To find out how many photons are emitted per second by a 5 mW laser source operating at a wavelength of 632.8 nm, we can follow these steps:

### Step 1: Convert the power of the laser from milliwatts to watts.
The power of the laser is given as 5 mW. We need to convert this to watts:

\[ \text{Power} = 5 \, \text{mW} = 5 \times 10^{-3} \, \text{W} \]

### Step 2: Convert the wavelength from nanometers to meters.
The wavelength is given as 632.8 nm. We convert this to meters:

\[ \text{Wavelength} = 632.8 \, \text{nm} = 632.8 \times 10^{-9} \, \text{m} \]

### Step 3: Calculate the energy of a single photon.
The energy of a single photon can be calculated using the formula:

\[ E = \frac{hc}{\lambda} \]

Where:
- \( h = 6.626 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 632.8 \times 10^{-9} \, \text{m} \)

Substituting the values:

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{632.8 \times 10^{-9} \, \text{m}} \]

Calculating this gives:

\[ E \approx 3.14 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second.
The number of photons emitted per second can be calculated by dividing the power of the laser by the energy of a single photon:

\[ \text{Number of photons per second} = \frac{\text{Power}}{E} \]

Substituting the values:

\[ \text{Number of photons per second} = \frac{5 \times 10^{-3} \, \text{W}}{3.14 \times 10^{-19} \, \text{J}} \]

Calculating this gives:

\[ \text{Number of photons per second} \approx 1.6 \times 10^{16} \, \text{photons/s} \]

### Final Answer:
The number of photons emitted per second by a 5 mW laser source operating at 632.8 nm is approximately \( 1.6 \times 10^{16} \) photons/s.

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