Question

The lowest energy X-rays having $\lambda =3.055\times {10}^{-8}m$. Which of the following statements is/are true?

• A. The minimum difference in energy between two Bohr's orbits such that an electronic transition would correspond to the emission of an X-ray is $6.52\times {10}^{-18}J$
• B. For $Z=2$ the transiton that corresponds to the above radiation is $n=2$ to $n=1$
• C. For $Z=2$ the transiton that corresponds to the above radiation is $n=3$ to $n=2$
• D. The minimum difference in energy between two Bohr's orbits such that an electronic transition would correspond to the emission of an X-ray is $1.65\times {10}^{18}J$

Answer 1

Answer: (A), (B)

For $Z=2$ the transiton that corresponds to the above radiation is $n=2$ to $n=1$

$\Delta E=\frac{hc}{\lambda }=\frac{(6.63\times {10}^{-34}J.s)\times (3\times {10}^{8}m/s)}{3.055\times {10}^{-8}m}$
$=6.52\times {10}^{-18}J$
$\Delta E_H=\frac{3}{4}(2.176\times {10}^{-18})J$
$=1.63\times {10}^{-18}$
$\Delta E=\Delta E_H(Z{)}^2$
$Z^2=\frac{\Delta E}{\Delta E_H}=\frac{6.52\times {10}^{-18}}{1.63\times {10}^{-18}}=4$
$Z=2$