Question

Through appropriate calculations, compare the energy associated with one mole of photons of gamma radiation (of wavelength 3.56 x 10-11 m) and one mole of photons of short-wave radio waves (of wavelength 12 cm).

Answer 1

We can use the following formula to calculate energy, E.

E=hv = hc/ƛ, where. h is Planck’s constant = 6.626x10⁻³⁴J.s, c is the velocity of light = 3x10⁸ms⁻¹ and ƛ is the wave length of the photon.

For gamma radiation, E = (6.626x10⁻³⁴J.s x 3x10⁸ms⁻¹)/ 3.56 x 10^-11 m =5.583e-15 J per photon.

We know 1 mole of photon = Avogardro’s number of photons.

Therefore energy in 1 mole of gamma radiation = 6.023e23*5.583e-15 J/mol = 3362.640e6 J/mol

For radio waves, E= (6.626x10⁻³⁴J.s x 3x10⁸ms⁻¹)/0.12m =1.6565e-24 J per photon.

Therefore energy in 1 mole of radio wave = 6.023e23*1.6565e-24 J/mol =0.99770995 J/mol

So, the gamma radion has 3.37035829 × 10⁹ (3362.640e6 J/mol/0.99770995 J/mol) times more energy than the radio wave.