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: Understand power rating.
Power of bulb is: \[ 150\ watt. \] Since: \[ 1\ watt=1\ J/s, \] the bulb consumes: \[ 150\ J/s. \]

Step 2: Calculate energy converted into light.
Only \(8%\) of energy is converted into light. Therefore, light energy emitted per second is: \[ \frac{8}{100}\times150. \] \[ =12\ J/s. \]

Step 3: Use energy of one photon.
Energy of one photon is: \[ 4.42\times10^{-19}J. \] Number of photons emitted per second: \[ n=\frac{\text{total light energy per second}}{\text{energy of one photon}}. \] \[ n=\frac{12}{4.42\times10^{-19}}. \]

Step 4: Calculate value.
\[ n=2.714\times10^{19}. \] Approximately: \[ n=2.71\times10^{19}. \] Therefore, the number of photons emitted per second is: \[ 2.71\times10^{19}. \]