Please give explanation Exposure to a sufficient quantity of ultraviolet light w
ID: 1552829 • Letter: P
Question
Please give explanation
Exposure to a sufficient quantity of ultraviolet light will redden the skin, producing erythema___a sunburn. The amount of exposure necessary to produce this reddening depends on the wavelength. For a 1.0 cm^2 patch of skin, 3.7 mJ of ultraviolet light at a wavelength of 254 nm will produce reddening at 300 nm wavelength, 13 mJ are required. a. What is the photon energy corresponding to each of these wavelengths? b. How many total photons does each of these exposures correspond to? c. Explain why there is a difference in the number of photons in the two cases.Explanation / Answer
A. The formula is E = hv
where h = Plancks constant = 6.626*10^-34 J s and v = frequency
For 254 nm, frequency = velocity/wavelength (velocity = c = 3*10^8 m/s)
= 3*10^8/(254*10^-9)
= 0.0118*10^17 s^-1
E = 6.626*10^-34*0.0118*10^17 J
E = 0.0782*10^-17 J
E = 7.82*10^-19 J Answer
B. and for 3.7*10^-3 J/cm^2 requires 3.7*10^-3/7.82*10^-19 photons/cm^2
= 0.473*10^16 photons/cm^2
for 300 nm wavelength, frequency = 3*10^8/300*10^-9 = 0.01*10^17s^-1
E = 6.626*10^-34*0.01*10^17 J
= 6.63*10^-19 J Answer
C. and for 13*10^-3 J/cm^3 requires 13*10^-3/6.63*10^-19 photons/cm^2
= 1.961*10^16 photons/cm^2