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Question: A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emit...

A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb.

A

3×1020s−13 \times 10^{20}s^{- 1}

B

2×10−20s−12 \times 10^{- 20}s^{- 1}

C

2×1020s−12 \times 10^{20}s^{- 1}

D

1×10−20s−11 \times 10^{- 20}s^{- 1}

Answer

2×1020s−12 \times 10^{20}s^{- 1}

Explanation

Solution

: Power of the bulb = 100 watt = 100 J s−1s^{- 1}

Energy of one photon, E = hυ=hc/λh\upsilon = hc/\lambda

=6.626×10−34Js×3×108ms−1400×10−9m= \frac{6.626 \times 10^{- 34}Js \times 3 \times 10^{8}ms^{- 1}}{400 \times 10^{- 9}m}

=4.969×10−19J= 4.969 \times 10^{- 19}J

Number of photons emitted

=100Js−14.969×10−19J=2.012×1020s−1= \frac{100Js^{- 1}}{4.969 \times 10^{- 19}J} = 2.012 \times 10^{20}s^{- 1}