Human skin is most sensitive to ultraviolet light of approximate wavelength 300

Question

Human skin is most sensitive to ultraviolet light of approximate wavelength 300 nm (

(a) Find the energy of a single photon of such light

(b) The threshold for sunburn occurs when 1 cm2 of skin absorbs about 1015 of these UV photons over an interval of several hours or less. How much energy is absorbed?

(c)What is the intensity of the UV light if it delivers this much energy in 38.0 minutes? (By way of comparison, the ultraviolet component of sunlight normally incident on the earth's surface at sea level ranges in wavelength from 310 nm to 400 nm, with a total intensity of about 40 W/m2.)

Explanation / Answer

(a)

Energy of the single photon is

E = hc / lamda

E = (6.63*10^-34 J.s)*(3.0*10^8 m/s) / ( 300*10^-9 m)

E = 6.63*10^-19 J

(b)

The energy absorbed by the skin is

Es = NE = 10^15 * 6.63*10^-19 J = 673*10^-6 J

(c)

The intensity of light is

I = Es/At

where A is area and t is time

I = (673*10^-6 J)/(10^-4 m^2)(38*60 s)

I = 2.95 *10^-3 W/m^2

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