The wavelength of `k_(alpha) ` X- rays produced by an X - rays tube is `0.76 Å` . The atomic number of the anode material of the tube is …….

Options

A. 20
B. 60
C. 41
D. 80

Answer

C

Explanation

Given , wavelelngth`lambda_(K_(alpha))=0.76Å=0.76xx10^(-10)m`
Moseley's empirical formula for `K_(alpha)` X-rays when adapted to Bohr model is given by
`" " hv_(K_(alpha))=(3)/(4)xx13.6(Z-1)^(2)eV`
`" " (hc)/(lambda_(K_(alpha)))=(3)/(4)xx13.6xx1.6xx10^(-19)(Z-1)^(2)J " " [ :. 1eV =1.6xx10^(-19)J]`
`rArr(6.626xx10^(-34)xx3xx10^(5))/(0.76xx10^(-10))=16.08xx10^(-19)(Z-1)^(2) " " [ :. h=6.626xx10^(-34)J-s and c=3xx10^(8)ms^(-1)]`
`rArr" " 26.15xx10^(-16)=16.08xx10^(-19)(Z-1)^(2)`
`rArr" " 1.63xx10^(3)=(Z-1)^(2)rArr16.3xx10^(2)=(Z-1)^(2)`
`rArr" " Z-1=40.4`
`:. " " Z=40.4+1~~41`