The energy of an electron in the ground state ( n = 1 ) for He + ion is - x J, then that for an electron in n = 2 state for Be 3 + ion in J is [2024]

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Solution

Q.
The energy of an electron in the ground state $(n = 1)$ for ${He}^{+}$ ion is $- x$ J, then that for an electron in $n = 2$ state for ${Be}^{3 +}$ ion in J is [2024]

1 $- x$

2 $- \frac{x}{9}$

3 $- 4 x$

4 $- \frac{4}{9} x$

Ans.
(1)

$E_{n} = - R_{H} \frac{Z^{2}}{n^{2}}$

For ground state $H e^{+}$ ion, Z = 2, n = 1,

$E_{1} = - R_{H} \frac{2^{2}}{1^{2}} = - 4 R_{H} = - x J$

For an electron in n = 2 state for $B e^{3 +}$ ion (Z = 4),

$E_{2} = - R_{H} \frac{4^{2}}{2^{2}} = - 4 R_{H} = - x J$

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