Question

How much energy is contained in 1 mol of γ-ray photons with a wavelength of 2.68×10−5 nm

Answer 1

1. Convert nm to m

1 nm = 10^-9 m

2.68 x 10^-5 nm = (2.68 x 10^-5) x 10^-9 m = 2.68 x 10^-14 m

2. Use formula E=hc/wavelength (where, h = 6.63 x 10^-34Js, c = 3 x 10⁸ m/s)

E = { (6.63 x 10^-34Js) (3 x 10⁸ m/s) } / (2.68 x 10^-14 m)

= 53.31 x 10^-12J

3. Convert J to kJ

   1 J = 10^-3kJ

53.31 x 10^-12J = 53.31 x 10^-12​ x 10^-3 kJ

​    = 53.31 x 10^-15 kJ
4. Multiply by Avogadro's number

(6.02 x 10²³) x (53.31 x 10^-15 kJ)

= 3.21 x 10¹⁰​ kJ