If the lowest energy X-rays have $λ$ = 3.055 × 10^–8m, 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 from the second energy level to the first result in the emission of an X-ray?

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answer is B.

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Detailed Solution

$ΔE = \frac{hc}{λ}$
$\begin{array}{l} = \frac{(6 .63 \times 10^{- 34} J - s) (3 .00 \times 10^{8} m / s)}{3 .055 \times 10^{- 8} m} = 6 .52 \times 10^{- 18} J \\ {ΔE}_{H} = \frac{3}{4} (2 .176 \times 10^{- 18} J); \\ {ΔE}_{H} = 1 .63 \times 10^{- 18} J; ΔE = {ΔE}_{H} (Z^{2}) \\ Z^{2} = \frac{ΔE}{{ΔE}_{H}} = \frac{(6 .52 \times 10^{- 18})}{(1 .63 \times 10^{- 18})} = 4 \\ Z = 2 (helium) \end{array}$