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 of the laser to watts
The power of the laser is given as 2 mW (milliwatts). We need to convert this to watts:
\[ \text{Power} = 2 \, \text{mW} = 2 \times 10^{-3} \, \text{W} \]

### Step 2: Convert the wavelength from nanometers to meters
The wavelength is given as 500 nm. We need to convert this to meters:
\[ \text{Wavelength} = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

### 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:
- \(h = 6.6 \times 10^{-34} \, \text{Js}\) (Planck's constant)
- \(c = 3.0 \times 10^{8} \, \text{m/s}\) (speed of light)
- \(\lambda = 5 \times 10^{-7} \, \text{m}\) (wavelength)

Substituting the values:
\[ E = \frac{(6.6 \times 10^{-34}) \times (3.0 \times 10^{8})}{5 \times 10^{-7}} \]

### Step 4: Perform the calculation for energy
Calculating the numerator:
\[ 6.6 \times 10^{-34} \times 3.0 \times 10^{8} = 1.98 \times 10^{-25} \, \text{Jm} \]
Now divide by the wavelength:
\[ E = \frac{1.98 \times 10^{-25}}{5 \times 10^{-7}} = 3.96 \times 10^{-19} \, \text{J} \]

### Step 5: Calculate the number of photons emitted per second
The number of photons \(n\) emitted per second can be calculated using the formula:
\[ n = \frac{\text{Power}}{E} \]
Substituting the values:
\[ n = \frac{2 \times 10^{-3}}{3.96 \times 10^{-19}} \]

### Step 6: Perform the final calculation
Calculating \(n\):
\[ n \approx \frac{2 \times 10^{-3}}{3.96 \times 10^{-19}} \approx 5.06 \times 10^{15} \]

### Step 7: Round to appropriate significant figures
Rounding \(5.06 \times 10^{15}\) gives approximately \(5 \times 10^{15}\).

### Final Answer
The number of photons emitted per second is:
\[ \boxed{5 \times 10^{15}} \]