Question

Number of photons emitted by 10 watt bulb in 10 seconds, if wavelength of light is 1000 \(\AA\) is

• A. $1.01\times10^{11}$
• B. $2.02\times10^{13}$
• C. $3.03\times10^{15}$
• D. $4.04\times10^{19}$

Hint:

Use conversion 1\AA = \(10^{-10}\) m carefully.

Answer 1

The Correct Option is D

Step 1: Energy of one photon \[ E=\frac{hc}{\lambda}. \] Take \(h=6.6\times10^{-34}\) J·s, \(c=3\times10^8\) m/s, \(\lambda=1000\) \AA\ = \(1\times10^{-7}\) m. \[ E= \frac{6.6\times10^{-34}\times3\times10^8}{1\times10^{-7}} =1.98\times10^{-18}\text{ J}. \]
Step 2: Total energy from bulb \[ P t = 10\times10=100\text{ J}. \]
Step 3: Number of photons \[ N=\frac{100}{1.98\times10^{-18}} =5.05\times10^{19}. \]
Step 4: Closest option (D).