Question

The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which (a) an electron, and (b) a neutron, would have the same de Broglie wavelength.

Answer 1

relation between De-broglie's wavelength and kinetic energy is K = h²/2mλ²

(a) an electron

mass of electron, m = 9.1 × 10^-31 Kg

wavelength, λ = 589nm = 589 × 10^-9m

Plank's constant, h = 6.63 × 10^-34 J.s

so, kinetic energy K = (6.63 × 10^-34)²/{2 × 9.1 × 10^-31 × (589 × 10^-9)²}

= 6.95 × 10^-25 J

we know, 1eV = 1.6 × 10^-19 J

so, kinetic energy, K = 6.95 × 10^-25/(1.6 × 10^-19) = 4.34 × 10^-6 eV = 4.34μeV

similarly, (b) kinetic energy of neutron to have De-broglie's wavelength of 589nm

K = h²/2mλ²

here, m = mass of neutron = 1.67 × 10^-27 Kg

so, K = (6.63 × 10^-34)²/{(2 × 1.67 × 10^-27 × (589 × 10^-9)²}

= 3.78 × 10^-28 J or, 2.36 neV