If the lowest energy X-rays have `lambda=3.055xx10^(-8)` m, estimate the minimum difference in energy between two Bohr's orbits such that an electronic transition would correspond to the emission of an X-ray. Assuming that the electrons in other shells exert no influence, at what Z (minimum) would a transition form the second level to the first result in the emission of an X-ray?

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

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