Question
A 100 watt bulb emits monochromatic light of wavelength 400$$\,nm.$$ Calculate the number of photons emitted per second by the bulb.
A.
$$3 \times {10^{20}}{s^{ - 1}}$$
B.
$$2 \times {10^{ - 20}}{s^{ - 1}}$$
C.
$$2 \times {10^{20}}{s^{ - 1}}$$
D.
$$1 \times {10^{ - 20}}{s^{ - 1}}$$
Answer :
$$2 \times {10^{20}}{s^{ - 1}}$$
Solution :
$$\eqalign{
& {\text{Power of the bulb}} = 100\,watt = 100\,J\,{s^{ - 1}} \cr
& {\text{Energy of one photon}}\,\,E = h\upsilon = \frac{{hc}}{\lambda } \cr
& = \frac{{6.626 \times {{10}^{ - 34}}Js \times 3 \times {{10}^8}m\,{s^{ - 1}}}}{{400 \times {{10}^{ - 9}}\,m}} \cr
& = 4.969 \times {10^{ - 19}}\,J \cr
& {\text{Number of photons emitted}} \cr
& = \frac{{100\,J\,{s^{ - 1}}}}{{4.969 \times {{10}^{ - 19}}J}} \cr
& = 2.012 \times {10^{20}}{s^{ - 1}} \cr} $$