First slide

Hydrogen -like ion

Question

An electron revolve round the nucleus of charge Ze. In order to excite the electron from state n=2 to n=3 the energy required is 47.2 eV. What is the value of Z ?

Easy

A

$Z \equiv 5$
B

$Z \equiv 4$
C

$Z \equiv 3$
D

$Z \equiv 2$

Solution

Energy of H atom = $13.6 (\frac{1}{4} - \frac{1}{9}) = 1.89 eV$
$Z^{2} = \frac{47.2}{1.89} = 24.47 \equiv 25 \Rightarrow Z \equiv 5$

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