To solve the problem of how many photons are emitted by a laser source of \(5 \times 10^{-3}\) W operating at 632.2 nm in 2 seconds, we can follow these steps:
### Step 1: Calculate the total energy emitted by the laser in 2 seconds.
The formula to calculate energy is given by:
\[
E = P \times t
\]
where \(E\) is the energy, \(P\) is the power of the laser, and \(t\) is the time.
Given:
- \(P = 5 \times 10^{-3} \, \text{W}\)
- \(t = 2 \, \text{s}\)
Substituting the values:
\[
E = 5 \times 10^{-3} \, \text{W} \times 2 \, \text{s} = 10 \times 10^{-3} \, \text{J} = 10^{-2} \, \text{J}
\]
### Step 2: Calculate the energy of one photon.
The energy of one photon can be calculated using the formula:
\[
E_p = \frac{h \cdot c}{\lambda}
\]
where:
- \(E_p\) is the energy of one photon,
- \(h = 6.63 \times 10^{-34} \, \text{Js}\) (Planck's constant),
- \(c = 3 \times 10^8 \, \text{m/s}\) (speed of light),
- \(\lambda = 632.2 \, \text{nm} = 632.2 \times 10^{-9} \, \text{m}\) (wavelength).
Substituting the values:
\[
E_p = \frac{6.63 \times 10^{-34} \, \text{Js} \times 3 \times 10^8 \, \text{m/s}}{632.2 \times 10^{-9} \, \text{m}}
\]
Calculating \(E_p\):
\[
E_p = \frac{1.989 \times 10^{-25}}{632.2 \times 10^{-9}} \approx 3.15 \times 10^{-19} \, \text{J}
\]
### Step 3: Calculate the number of photons emitted.
The number of photons \(n\) emitted can be calculated using the formula:
\[
n = \frac{E}{E_p}
\]
Substituting the values:
\[
n = \frac{10^{-2} \, \text{J}}{3.15 \times 10^{-19} \, \text{J}} \approx 3.17 \times 10^{16}
\]
### Conclusion
Thus, the number of photons emitted by the laser source in 2 seconds is approximately:
\[
n \approx 3.17 \times 10^{16}
\]
