Question

The UV light that is responsible for tanning the skin falls in the 320-nm to 400-nm region. Calculate the total energy (in joules) absorbed by a person exposed to this radiation for 2.5 h, given that there are 2.0 × 1016 photons hitting Earth’s surface per square centimeter per second over a 80-nm (320-nm to 400-nm) range and that the exposed body area is 0.45 m2. Assume that only half of the radiation is absorbed and the other half is reflected by the body. (Hint: Use an average wavelength of 360 nm in calculating the energy of a photon.)

Answer 1

Answer:

Total Energy 25 j/s

Explanation:

Given Data:

UV light wavelength range 320 nm - 400 nm

Duration of radiation 2.5 h

Exposed area $0.45 m^2 = 4500 cm^2$

Number of photons $2.0\times 10^{16}$

Average wavelength $= \frac{320 + 400}{2} = 360\times 10^{-9} m$

Energy per photon $=\frac{hc}{average\ wavelenght}$

                               $= \frac{6.626\times 10^{-34}\times 3\times 10^8}{360\times 10^{-9}}$

                               $=5.522 \times 10^{-22} J$

Total photon hitting the ground  $= 2.0\times 10^{16} \times 4500 = 9.9\times 10^{19} photons$

Number of photons observed  $= \frac{9.9\times 10^{19}}{2} = 4.5 \times 10^{19} photons$

Total ENERGY $= 4.5 \times 10^{19} \times 5.522 \times 10^{-22} = 25 J/s$