Monochromatic light of wavelength `667 nm` is produced by a helium neon laser . The power emitted is `9 mW` . The number of photons arriving per second on the average at a target irradiated by this beam is

Options

A. `9 xx 10^(17)`
B. `3 xx 10^(16)`
C. `9 xx 10^(15)`
D. `3 xx 10^(19)`

Answer

To find the number of photons arriving per second at a target irradiated by a helium-neon laser emitting monochromatic light of wavelength 667 nm and power 9 mW, we can follow these steps:

### Step 1: Convert the power from milliwatts to watts
The power \( P \) is given as 9 mW. We can convert this to watts:
\[ P = 9 \, \text{mW} = 9 \times 10^{-3} \, \text{W} \]

### Step 2: Convert the wavelength from nanometers to meters
The wavelength \( \lambda \) is given as 667 nm. We can convert this to meters:
\[ \lambda = 667 \, \text{nm} = 667 \times 10^{-9} \, \text{m} \]

### Step 3: Calculate the energy of a single photon
The energy \( E \) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \) (Planck's constant) = \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( c \) (speed of light) = \( 3 \times 10^8 \, \text{m/s} \)

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{667 \times 10^{-9} \, \text{m}} \]
Calculating this gives:
\[ E \approx 2.98 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons per second
The number of photons \( n \) arriving per second can be calculated using the formula:
\[ n = \frac{P}{E} \]
Substituting the values:
\[ n = \frac{9 \times 10^{-3} \, \text{W}}{2.98 \times 10^{-19} \, \text{J}} \]
Calculating this gives:
\[ n \approx 3.02 \times 10^{16} \, \text{photons/s} \]

### Final Answer
The number of photons arriving per second at the target is approximately:
\[ \boxed{3.02 \times 10^{16}} \, \text{photons/s} \]

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