The wavelength of light 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

de Broglie wavelength, `lamda = (h)/(sqrt(2mE)) or, E = (1)/(2m). (h^(2))/(lamda^(2))`
(a) Kinetic energy of electron,
`E_(e) = (1)/(2 xx 9.1 xx 10^(-31)) xx ((6.626 xx 10^(-34))/(589 xx 10^(-9)))^(2)`
`= 6.95 xx 10^(-25)J`
(b) Kinetic energy of neutron,
`E_(n) = (1)/(2 xx 1.67 xx 10^(-27)) xx ((6.626 xx 10^(-34))/(589 xx 10^(-9)))^(2)`
`= 3.79 xx 10^(-28)J`