How many photons are emitted per second by a `5 mW` laser operating at `620 nm`?

Answer

To solve the problem of how many photons are emitted per second by a 5 mW laser operating at 620 nm, we will follow these steps:

### Step 1: Convert the power of the laser from milliwatts to watts
Given:
- Power (P) = 5 mW = 5 × 10^(-3) W

### 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:
- \( h \) (Planck's constant) = \( 6.626 \times 10^{-34} \) J·s
- \( c \) (speed of light) = \( 3.00 \times 10^{8} \) m/s
- \( \lambda \) (wavelength) = 620 nm = \( 620 \times 10^{-9} \) m

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J·s}) \times (3.00 \times 10^{8} \, \text{m/s})}{620 \times 10^{-9} \, \text{m}} \]

Calculating the numerator:
\[ 6.626 \times 10^{-34} \times 3.00 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J·m} \]

Now, dividing by the wavelength:
\[ E = \frac{1.9878 \times 10^{-25}}{620 \times 10^{-9}} = 3.20 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the number of photons emitted per second
The number of photons emitted per second (N) can be calculated using the formula:
\[ N = \frac{P}{E} \]
Where:
- \( P \) = power of the laser in watts
- \( E \) = energy of a single photon in joules

Substituting the values:
\[ N = \frac{5 \times 10^{-3} \, \text{W}}{3.20 \times 10^{-19} \, \text{J}} \]

Calculating:
\[ N = \frac{5 \times 10^{-3}}{3.20 \times 10^{-19}} = 1.56 \times 10^{16} \, \text{photons/second} \]

### Final Answer:
The number of photons emitted per second by the 5 mW laser operating at 620 nm is approximately \( 1.56 \times 10^{16} \) photons/second.

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