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 ?

Options

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

Answer

B

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`
`DeltaE_H = 3/4 (2.176 xx 10^(-18) J)n,`
`Delta E_H = 1.63 xx 10^(-18) J , DeltaE = DeltaE_H (Z^2)`
`Z^2 = (DeltaE)/(DeltaE_H) =((6.52xx10^(-18))/(1.63xx10^(-18)))= 4 `,
Z= 2(helium)