In Bohr's theory of hydrogen atom , calculate the energy of the photon emitted during a transition of the electron from the first excited state to its ground state . Write in which region of the electromagnetic spectrum this transition lies . Given Rydbergy constant `R = 1.03 xx 10^(7) m^(-1)` .

Explanation

When in a hydrogen atom a transition takes place from the first excited state (n = 2) to its ground state (n = 1), we have
` (1)/(lambda) = R [(1)/((1)^(2)) - (1)/((2)^(2))] = (3R)/(4)`
`therefore ` Energy of photon `E= hv = (hc)/(lambda) = (hc.3R)/(4) J = (3hcR)/(4 e)eV`
`rArr " " E= (3xx 6.63 xx 10^(-34) xx 3xx 10^(8) xx 1.03 xx 10^(7))/(4 xx 1.6 xx 10^(-9)) eV = 9.6 eV`
The transition lies in the ultraviolet region of electromagnetic spectrum and corresponds to first line of Lyman series.