(a) State Bohr's postulate to define stable orbits in hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits ?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to then n = 4 level . Estimate the frequeny of the photon.

Explanation

Energy in the n=4 level` = ( -E_0)/( 4^(2)) =( E_0)/( 16) `
` therefore ` Energy required to take the electron form the ground state , to the n= 4 level `= ((E_0)/( 16)) -(-E_0)`
`= ( -1+16)/( 16) `
`= ( 15)/( 16) E_0`
` =( 15)/( 16) xx 13.6xx 1.6 xx 10 ^(-19) J`
Let the frequency of the photon be, v we have
` hv= (`15)/( 16) xx 13.6xx 1.6xx10 ^(-19) `
` therefore v= ( 15xx 13.6xx 1.6xx10 ^(-19))/( 16xx6.63xx10^(-34))` Hz
`= 3.1xx 10 ^(15) Hz`
(Also accept `3xx10 ^(15) Hz)`