In the Bohr model of the hydrogen atom, what is the de-Broglie wavelength for the electron when it is in (a) the n=1 level?
(b) Then n=4 level? In each case, compare the de-Broglie wavelength to the circumference `2pir_n` of the orbit.

Answer

A, B, C

Explanation

(a) `E_1 = -13.6 eV
`:. KE = |E_1| = 13.6 eV`
`lambda_1 (in Å`) = sqrt((150)/(KE(in eV)) for an electron`
`=sqrt(150)/(13.6) =3.32 Å`
`2pir_1 = 2pi(0.529 Å) ~~ 3.32 Å`
(b) `E_4 =(E_1)/((4))^2 = (-13.6)/((4))^2 = - 0.85 eV`
`lambda_4 = sqrt((150)/(0.85)) as KE = |E_4| = 0.85 eV`
`~~13.3 Å
`2pir_4 = 2pi(n)^2 r_1 (as r prop n^2)`
`=53.15 Å = 4lambda_4.`