MCQ
The energy of an electron in the ground state $(n=1)$ for $\mathrm{He}^{+}$ion is $-x ~J$, then that for an electron in $n=2$ state for $Be^{3+}$ ion in $J$ is
  • A
    $-\frac{x}{9}$
  • B
     $-4 x$
  • C
     $-\frac{4}{9} x$
  •  $-x$

Answer

Correct option: D.
 $-x$
d
$E_n=-R_H\left(\frac{Z^2}{n^2}\right) J$

For $\mathrm{He}^{+}(n=1)$,

$E_n $$ =-x=-R_H\left(\frac{2^2}{1^2}\right)=-4 R_H $

$\therefore \quad R_H $$=\frac{x}{4}$

For $B^{3+}(n=2), $

$E_n $$ =-R_H\left(\frac{z^2}{n^2}\right) J $

$ =-\frac{x}{4} \times\left(\frac{4 \times 4}{2 \times 2}\right)=-\times \mathrm{J}$

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