Question

A $100\, watt$ bulb emits monochromatic light of wavelength $400\, \mathrm{nm}$. The number of photons emitted by the bulb per second is

• A. $2 \times 10^{10} \mathrm{~s}^{-1}$
• B. $2 \times 10^{20} \mathrm{~s}^{-1}$
• C. $3 \times 10^{10} \mathrm{~s}^{-1}$
• D. $3 \times 10^{20} \mathrm{~s}^{-1}$

Answer 1

Answer: (B)

Power of the bulb $=100$ watt $=100 \mathrm{~J} \mathrm{~s}^{-1}$
Energy of one photon
$E=h v=h c / \lambda$
$=\frac{6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s} \times \times 3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}}{400 \times 10^{-9} \mathrm{~m}}$
$=4.969 \times 10^{-19} \mathrm{~J}$
Number of photons emitted
$=\frac{100 \mathrm{~J} \mathrm{~s}^{-1}}{4.969 \times 10^{-19} \mathrm{~J}}$
$=2.012 \times 10^{20} \mathrm{~s}^{-1}$