Question

If `R_(H)` represents Rydberg constant, then the energy of the electron in the ground state of hydrogen atom is
A. `- (hc)/(R_(H))`
B. `- (1)/(R_(H) ch)`
C. `-R_(H) ch`
D. `- (R_(H)c)/(h)`

Answer 1

Correct Answer - C
According to Rydberg formula,
`bar(v) = R_(H) ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`....(i)
According to Bohr model, for an electronic transition,
`Delta E = - (2pi^(2) me^(4))/(h^(2)) ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
But `Delta E = hv = (hc)/(lamda) = hc bar(v)`
`:. hc bar(v) = - (2pi^(2) me^(4))/(h^(2)) ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
or `bar(v) = - (2pi^(2) me^(4))/(ch^(3)) ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`...(ii)
Comparing eqns. (i) and (ii)
`R_(H) = - (2pi^(2) me^(4))/(ch^(3)) :. E_(1) = - (2pi^(2) me^(4))/(h^(2)) = - R_(H) ch`