Question

A bulb is rated at \(150\ watt\), converting \(8%\) energy into light. If energy of one photon is \(4.42\times10^{-19}J\), how many photons are emitted by the bulb per second?

• A. \(1.35\times10^{19}\)
• B. \(2.71\times10^{19}\)
• C. \(27.2\times10^{19}\)
• D. \(4.06\times10^{19}\)

Hint:

Number of photons \(=\frac{\text{total energy emitted as light}}{\text{energy of one photon}}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Topic:
This question combines concepts from "Structure of Atom" and basic physics (Power and Energy). It deals with the quantization of energy, where light is viewed as a stream of individual particles called photons. We must calculate the total energy converted into light every second and then determine how many individual photons make up that total energy value.
Step 2: Key Formulas and Approach:

Power (Watts) = Energy per unit time (Joules per second).
Energy converted to light = $\text{Total Power} \times \text{Efficiency}$.
Total light energy per second ($E_{total}$) = $n \times E_{photon}$ (where $n$ is the number of photons).

Step 3: Detailed Explanation:

Total Energy Output: A 150 W bulb outputs 150 Joules of energy every second.
Efficiency Calculation: Only 8% of this energy is actually light. \[ \text{Light energy per second} = 150 \times 0.08 = 12 \text{ J/s} \]
Determine Photon Count (n): The energy of a single photon is given as $4.42 \times 10^{-19}$ Joules. \[ 12 = n \times (4.42 \times 10^{-19}) \] \[ n = \frac{12}{4.42 \times 10^{-19}} \]
Final Calculation: \[ n = 2.7149 \times 10^{19} \approx 2.71 \times 10^{19} \]
This huge number indicates the staggering amount of photons emitted by even a modest light source.
Step 4: Final Answer:
The number of photons emitted per second is \(2.71 \times 10^{19}\), matching option (A).