A 2 mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is: [Given Planck’s constant `h = 6.6 xx 10^(-34)Js`, speed of light `c = 3.0 xx 10^(8) m//s`]

Options

A. `5 xx 10^(15)`
B. `1 xx 10^(16)`
C. `2 xx 10^(16)`
D. `1.5 xx 10^(16)`

Explanation

To find the number of photons emitted per second by a 2 mW laser operating at a wavelength of 500 nm, we can follow these steps:

### Step 1: Convert the power from mW to W
The power of the laser is given as 2 mW. We need to convert this to watts (W):

\[ P = 2 \text{ mW} = 2 \times 10^{-3} \text{ W} \]

### Step 2: Convert the wavelength from nm to m
The wavelength is given as 500 nm. We need to convert this to meters (m):

\[ \lambda = 500 \text{ nm} = 500 \times 10^{-9} \text{ m} \]

### Step 3: Use the formula for energy of a single photon
The energy \(E\) of a single photon can be calculated using the formula:

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

Where:
- \(h\) is Planck's constant, \(6.6 \times 10^{-34} \text{ Js}\)
- \(c\) is the speed of light, \(3.0 \times 10^{8} \text{ m/s}\)

### Step 4: Calculate the energy of a single photon
Substituting the values into the formula:

\[ E = \frac{(6.6 \times 10^{-34} \text{ Js})(3.0 \times 10^{8} \text{ m/s})}{500 \times 10^{-9} \text{ m}} \]

Calculating the numerator:

\[ E = \frac{1.98 \times 10^{-25} \text{ Jm}}{500 \times 10^{-9} \text{ m}} = 3.96 \times 10^{-19} \text{ J} \]

### Step 5: Calculate the number of photons emitted per second
The number of photons \(n\) emitted per second can be calculated using the formula:

\[ n = \frac{P}{E} \]

Substituting the values:

\[ n = \frac{2 \times 10^{-3} \text{ W}}{3.96 \times 10^{-19} \text{ J}} \]

Calculating \(n\):

\[ n = \frac{2 \times 10^{-3}}{3.96 \times 10^{-19}} \approx 5.06 \times 10^{15} \]

### Final Answer
The number of photons emitted per second is approximately:

\[ n \approx 5.06 \times 10^{15} \]