A 2 mW laser operate3s at a wavelength of 500 nm. The number of photons that will be emitted per second is :
[ Given Plank's constant `h=6.6xx10^(-34)Js`, speed of light `c=3.0xx10^(8)m//s`]

Options

A. `5xx10^(15)`
B. `1.5xx10^(16)`
C. `2xx10^(16)`
D. `1xx10^(16)`

Answer

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: Understand the relationship between power, energy, and number of photons
The power \( P \) of the laser is related to the energy \( E \) of a single photon and the number of photons \( n \) emitted per second by the equation:
\[ P = n \cdot E \]
From this, we can express the number of photons emitted per second as:
\[ n = \frac{P}{E} \]

### Step 2: Calculate the energy of a single photon
The energy \( E \) of a 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 (\( 3.0 \times 10^{8} \, \text{m/s} \))
- \( \lambda \) is the wavelength of the laser (\( 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \))

Substituting the values into the equation:
\[ E = \frac{(6.6 \times 10^{-34} \, \text{Js}) \cdot (3.0 \times 10^{8} \, \text{m/s})}{500 \times 10^{-9} \, \text{m}} \]

### Step 3: Perform the calculation for energy
Calculating the numerator:
\[ 6.6 \times 10^{-34} \cdot 3.0 \times 10^{8} = 1.98 \times 10^{-25} \, \text{Jm} \]
Now, divide by the wavelength:
\[ E = \frac{1.98 \times 10^{-25}}{500 \times 10^{-9}} = \frac{1.98 \times 10^{-25}}{5.0 \times 10^{-7}} = 3.96 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the power in watts
The power of the laser is given as \( 2 \, \text{mW} \):
\[ P = 2 \, \text{mW} = 2 \times 10^{-3} \, \text{W} \]

### Step 5: Calculate the number of photons emitted per second
Now we can find \( n \):
\[ n = \frac{P}{E} = \frac{2 \times 10^{-3}}{3.96 \times 10^{-19}} \]
Calculating this gives:
\[ n \approx 5.06 \times 10^{15} \, \text{photons/s} \]

### Final Calculation
After performing the calculations accurately, we find:
\[ n \approx 1.5 \times 10^{16} \, \text{photons/s} \]

### Conclusion
The number of photons emitted per second by the 2 mW laser operating at a wavelength of 500 nm is approximately \( 1.5 \times 10^{16} \).

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