Question

The UV light that is responsible for tanning the skin falls in the 320− to 400−nm region. Calculate the total energy (in joules) absorbed by a person exposed to this radiation for 3.00 hours, given that there are 2.00 × 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 0.450 m2. Assume that only half of the radiation is absorbed and the other half is reflected by the body.

Answer 1

14,085 J

Step-by-step explanation:

For the range given (320 nm to 400 nm), the average wavelenght is

λ = (320 + 400)/2

λ = 360 nm

The energy of a single photon ca be calculated by:

E = h*c/λ

Where h is the Planck constant (h = 6.626x10⁻³⁴ J.s) and c is the speed of the light (c = 3.00x10⁸ m/s). So, for λ = 360 nm = 360x10⁻⁹ m

E = (6.626x10⁻³⁴*3.00x10⁸)/360x10⁻⁹

E = 3.13x10⁻¹⁶ J

The exposed body area is 0.450 m² x(100 cm/m)² = 4500 cm²

The total photons will be:

2.00x10¹⁶ photons/cm² * 4500 cm² = 9.00x10¹⁹ photons

So, the total energy of the photons is the energy of a single photon multiplied by the total photons:

Et = 3.13x10⁻¹⁶ * 9.00x10¹⁹

Et = 28170 J

Because only half of the radiation is absorbed, the total energy absorbed (Ea) is:

Ea = 28170/2

Ea = 14,085 J