The biological effects of a given dose of electromagnetic radiation generally be

Question

The biological effects of a given dose of electromagnetic radiation generally become more serious as the energy of the radiation increases. Infrared radiation has a pleasant warming effect to the skin, ultraviolet radiation causes tanning and burning of the skin, and X rays cause considerable tissue damage. Show how to determine (and then calculate) the amount of energy (per mole of photons) associated with each of these forms of electromagnetic radiation given that lambda = 1550 nm for infrared radiation v = 1.07 times 10^15 Hz for ultraviolet radiation, and lambda = 5.49 nm for X rays then rank these according to increasing energy.

Explanation / Answer

Energy and wavelength are related as E = hc/wavelength where

h-Planck's constant = 6.625x10-34J.sec

c-velcoity of light = 3.0x108 m

similarly with frequncey

E = h x frequency

1) energy of IR radiation

wavelength = 1550nm = 1550x 10-9 m

thus energy =6.625x10-34J.sec x 3.0x108 m / 1550x 10-9 m

= 1.282x10-19 J

The energy per mole of IR photons = avogadro number x energy of photon

= 6.203x1023 x1.282x10-19 J

= 7.95x104 J

= 79.5kJ

2)Energy of UV radiation

E = 6.625x10-34J.sec x1.07x 1015 /sec

= 7.088x10-19J

energy of one mole of UV photons = 6.023x1023 x7.088x10-19J

= 4.296x105 J

= 429.6 kJ

3)enegy of X- rays = 6.625x10-34J.sec x3.0x108 / 5.49x10-9 m

= 3.620x10-17 J

energy f one mole of X-ray photons= 6.203 x1023 x3.620x10-17 J

= 2.2456x106 J

= 2.2456x103 kJ

Thus in the increasing order of energy

IR < UV < x-rays

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