Exposure to a sufficient quantity of ultraviolet will redden the skin, producing

Question

Exposure to a sufficient quantity of ultraviolet 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 cm2 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.

Part A

What is the photon energy corresponding to the wavelength of 254 nm?

Express your answer using three significant figures.

Part B

What is the photon energy corresponding to the wavelength of 300 nm?

Express your answer using three significant figures.

Part C

How many total photons with the wavelength of 254 nm produce this reddening of the 1.0 cm2 of the skin?

Part D

How many total photons with the wavelength of 300 nm produce this reddening of the 1.0 cm2 of the skin?

Express your answer using two significant figures.

Explanation / Answer

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
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
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

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