Question

Calculate the energies of the photons associated with the following radiation:

1. violet light of 413 nm
2. X-rays of 0.1 nm
3. radio waves of 10 m

Answer 1

E = hv

E = `"hc"/λ` in Joule

E = `"hc"/(λe)` in eV

i. violet light of 413 nm

E = `(6.625 xx 10^-34 xx 3 xx 10^8)/(413 xx 10^-9 xx 1.6 xx 10^-19)`

= `19.875/660.8 xx 10^-26 xx 10^28`

= 0.032 × 10²

E = 3 eV

ii. X-rays of 0.1 nm

E = `(6.625 xx 10^-34 xx 3 xx 10^8)/(0.1 xx 10^-9 xx 1.6 xx 10^-19)`

= `(19.875 xx 10^-26)/(0.16 xx 10^-28)`

= 124.24 × 10²

E = 12424 eV

iii. radio waves of 10 m

E = `(6.625 xx 10^-34 xx 3 xx 10^8)/(10 xx 1.6 xx 10^-19)`

= `19.875/1.6 xx 10^-26 xx 10^-1 xx 10^19`

E = 1.24 × 10⁻⁷ eV