Number of photons having wavelength 632.8 nm, emitted by 5 mW laser source in 1 second is

Options

A. `1.6xx10^(19)`
B. `1.6xx10^(16)`
C. `1.6xx10^(25)`
D. `1.6xx10^(13)`

Answer

To find the number of photons emitted by a 5 mW laser source with a wavelength of 632.8 nm in one second, we can follow these steps:

### Step 1: Convert the wavelength from nanometers to meters
Given:
- Wavelength (λ) = 632.8 nm

To convert nanometers to meters:
\[ \lambda = 632.8 \, \text{nm} = 632.8 \times 10^{-9} \, \text{m} \]

### Step 2: Convert the power from milliwatts to watts
Given:
- Power (P) = 5 mW

To convert milliwatts to watts:
\[ P = 5 \, \text{mW} = 5 \times 10^{-3} \, \text{W} \]

### Step 3: Calculate the energy emitted in one second
Using the formula:
\[ \text{Energy (E)} = \text{Power (P)} \times \text{Time (t)} \]
Given that time (t) = 1 second:
\[ E = 5 \times 10^{-3} \, \text{W} \times 1 \, \text{s} = 5 \times 10^{-3} \, \text{J} \]

### Step 4: Use the formula to find the number of photons
The energy of one photon is given by:
\[ E = N \times \frac{hc}{\lambda} \]
Where:
- \( N \) = number of photons
- \( h \) = Planck's constant = \( 6.626 \times 10^{-34} \, \text{J s} \)
- \( c \) = speed of light = \( 3 \times 10^{8} \, \text{m/s} \)

Rearranging the formula to solve for \( N \):
\[ N = \frac{E \lambda}{hc} \]

### Step 5: Substitute the values into the equation
Substituting the values we have:
\[ N = \frac{(5 \times 10^{-3} \, \text{J}) \times (632.8 \times 10^{-9} \, \text{m})}{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})} \]

### Step 6: Calculate the number of photons
Calculating the numerator:
\[ 5 \times 10^{-3} \times 632.8 \times 10^{-9} = 3.164 \times 10^{-11} \, \text{J m} \]

Calculating the denominator:
\[ 6.626 \times 10^{-34} \times 3 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]

Now, substituting these values into the equation for \( N \):
\[ N = \frac{3.164 \times 10^{-11}}{1.9878 \times 10^{-25}} \approx 1.59 \times 10^{16} \]

### Final Answer
The number of photons emitted by the laser in one second is approximately:
\[ N \approx 1.6 \times 10^{16} \]