If the lowest energy X-rays have `lambda = 3.055 xx 10^(-8)m`, estimate the minimum difference in energy between two Bohr.s orbits such that an electronic transition would correspond to emission of an X-ray. Assuming that the electrons in other shells exert no influence, at what Z(minimum) would a transition from the second energy level to the first result in the emission of an X-ray ?

Answer

2

Explanation

`DeltaE = (hc)/(lambda) =(6.63 xx 10^(34) J - s) (3.00 xx 10^8 m//s)/(3.055xx10^(-8) m)`
`=6.52xx10^(-18) J`
`Delta E_H = 3/4 (2.176xx10^(-18) J ) = 1.63 xx 10^(-18) J`,
`Delta E = Delta E = Delta E_H (Z^2)`
`Z^2 = (DeltaE)/(Delta E_H) = (6.52xx10^(-18))/(1.63xx10^(-18)) = 4`
Z= 2 (helium)