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 each of these wavelengths

Answer 1

Energy = 7.83 x 10⁻¹⁹ J

Energy = 6.63 x 10⁻¹⁹ J

Step-by-step explanation:

The energy of a photon in terms of wavelength can be calculated by the following formula:

`Energy = (hc)/(\lambda)\\`

where,

h = Plank's Constant = 6.63 x 10⁻³⁴ Js

c = speed of light = 3 x 10⁸ m/s

λ = wavelength of light

Now, for λ = 254 nm = 2.54 x 10⁻⁷ m:

`Energy = ((6.63\ x\ 10^(-34)\ Js)(3\ x\ 10^8\ m/s))/(2.54\ x\ 10^(-7)\ m)\\`

Energy = 7.83 x 10⁻¹⁹ J

Now, for λ = 300 nm = 3 x 10⁻⁷ m:

`Energy = ((6.63\ x\ 10^(-34)\ Js)(3\ x\ 10^8\ m/s))/(3\ x\ 10^(-7)\ m)\\`

Energy = 6.63 x 10⁻¹⁹ J