If a monochromatic light source has a power output of $1 W$ (where $1 W=1 J/s$), and each photon has energy $E$, how many photons are emitted per second?

• A. $E\times 1$
• B. $\frac{1}{E}$
• C. $1+E$
• D. $\frac{E}{1}$

Answer: (B)

Verified step by step guidance

1. Identify the given quantities: the power output of the light source is 1 watt (W), which means it emits 1 joule (J) of energy per second (s). Each photon has an energy denoted by \( E \).
2. Recall the relationship between power, energy, and time: power \( P \) is the rate of energy transfer, so \( P = \frac{\text{energy}}{\text{time}} \). Here, the total energy emitted per second is 1 joule.
3. Understand that the total energy emitted per second is the sum of the energies of all photons emitted in that second. If \( N \) is the number of photons emitted per second, then the total energy per second is \( N \times E \).
4. Set up the equation relating power and photon energy: \( P = N \times E \). Since \( P = 1 \) watt, this becomes \( 1 = N \times E \).
5. Solve for the number of photons emitted per second \( N \) by rearranging the equation: \[ N = \frac{1}{E} \]. This gives the number of photons emitted per second in terms of the photon energy \( E \).