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Step-by-Step Solution
Step 1: Identify the Known Quantities
• Frequency of the light, $v = 6.0 \times 10^{14}\,\text{Hz}$
• Power of the laser, $P = 2 \times 10^{-3}\,\text{W}$
• Planck's constant, $h = 6.6 \times 10^{-34}\,\text{J·s}$ (approx.)
Step 2: Formula for the Energy of One Photon
The energy $E$ of a single photon of frequency $v$ is given by:
$$
E = h \times v
$$
Step 3: Calculate the Energy of One Photon
Substitute $h$ and $v$ into the formula:
$$
E = (6.6 \times 10^{-34}) \times (6.0 \times 10^{14})\,\text{J}
$$
$$
E = 6.6 \times 6.0 \times 10^{-34+14}\,\text{J}
$$
$$
E = 39.6 \times 10^{-20}\,\text{J} \approx 3.96 \times 10^{-19}\,\text{J}
$$
Step 4: Determine the Number of Photons per Second
Since power $P$ is the energy emitted per second, the number of photons $n$ emitted per second is:
$$
n = \frac{P}{E}
$$
Substituting the values:
$$
n = \frac{2 \times 10^{-3}}{3.96 \times 10^{-19}}
$$
Simplify:
$$
n \approx 0.505 \times 10^{16} = 5.05 \times 10^{15}
$$
Rounding suitably:
$$
n \approx 5 \times 10^{15}
$$
Step 5: Final Answer
The number of photons emitted on average by the source per second is $5 \times 10^{15}$.
