Question

Energy from the sun is received on earth at the rate of 2 cal $ cm^{ - 2} \, min^{ - 1}$. If average wavelength of solar light be taken at 5500 $\mathring{A}$ then how many photons are received on the earth $ cm^{ - 2} \, min^{ - 1} $ ?
$ ( h = 6.6 \times 10^{ - 34 }$ Js, 1 cal =$ 4.2 \, J )$

• A. $ 1.5 \times 10^{ 13} $
• B. $ 2.9 \times 10^{ 13} $
• C. $ 2.3 \times 10^{ 19} $
• D. $ 1.75 \times 10^{ 19} $

Answer 1

Answer: (C)

Energy received from the sun
= 2 cal $ cm^{ - 2} \, ( min)^{ - 1} $
= $ 8.4 \, J \, cm^{ - 2} \, ( min)^{ - 1} $
Energy of 1 photon received from sun,
E = $ \frac{ hc }{ \lambda } = \frac{ 6.6 \times 10^{ - 34} \times 3 \times 10^8 }{ 5500 \times 10^{ - 10 }} $
= $ 3.6 \times 10^{ - 19 } $ J
$ \therefore $ Number of photons reaching the earth per $cm^2$ per minute will be
n = $ \frac{ energy \, received \, from \, sun }{ energy \, of \, one \, photon } $
n = $ \frac{ 8.4 }{ 3.6 \times 10^{ - 19 }} = 2.3 \times 10^{ 19 } $