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.

Explanation

(a) `lambda_(e) = (12.27^(@))/(sqrt(v_(a))) A rArr v_(a) = (150)/(lambda_(e)^(2)) = (150)/((5890)^(2)) = 4.32 mu` V
`therefore `K.E = `eV_(a) = 4.32 mu `eV
(b) ` lambda = (h)/(p) = (h)/(sqrt(2m_(n) K.E)) rArr " K.E" = (h^(2))/(2m_(n)(lambda^(2)))`