A helium-neon laser has a power output of 1mW of light of wavelength 632.8 nm.
Q. Determine the number of photons emitted by the laser each second.

Options

A. `3.18xx10^(15)`
B. `4.5xx10^(16)`
C. `1.2xx10^(15)`
D. `2.9xx10^(17)`

Explanation

To determine the number of photons emitted by a helium-neon laser each second, we can follow these steps:

### Step 1: Understand the given data
We have:
- Power output of the laser, \( P = 1 \, \text{mW} = 1 \times 10^{-3} \, \text{W} \)
- Wavelength of the light, \( \lambda = 632.8 \, \text{nm} = 632.8 \times 10^{-9} \, \text{m} \)

### Step 2: Calculate the energy of one photon
The energy \( E \) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) (Planck's constant) \( = 6.626 \times 10^{-34} \, \text{J s} \)
- \( c \) (speed of light) \( = 3 \times 10^8 \, \text{m/s} \)

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{632.8 \times 10^{-9} \, \text{m}} \]

### Step 3: Calculate the energy of one photon
Now, performing the calculation:
\[ E = \frac{(6.626 \times 10^{-34})(3 \times 10^8)}{632.8 \times 10^{-9}} \]
\[ E \approx \frac{1.9878 \times 10^{-25}}{632.8 \times 10^{-9}} \]
\[ E \approx 3.14 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second
Using the relationship between power, number of photons, and energy:
\[ P = n \cdot E \]
where \( n \) is the number of photons emitted per second. Rearranging gives:
\[ n = \frac{P}{E} \]

Substituting the values:
\[ n = \frac{1 \times 10^{-3} \, \text{W}}{3.14 \times 10^{-19} \, \text{J}} \]
\[ n \approx 3.18 \times 10^{15} \, \text{photons/second} \]

### Final Answer
The number of photons emitted by the laser each second is approximately \( 3.18 \times 10^{15} \) photons.

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