MCQ
Radius of $1^{\text {st }}$ orbit of $H$ and some orbit of $Be ^{3+}$ is same . Energy of their orbit of $Be ^{3+}$ is ............$eV$
  • $-54.4$
  • B
    $-13.6$
  • C
    $-108.8$
  • D
    $-27.2$

Answer

Correct option: A.
$-54.4$
a
The radius of $n ^{ th }$ orbit is,

$r_{n} \propto \frac{n^{2}}{Z}$

$\left( r _{1}\right)_{ H }=\left( r _{ n }\right)_{ Be ^{3-}}$

$\frac{1^{2}}{1}=\frac{ n ^{2}}{4}$

$n =2$

The energy of their orbit is,

$( E )_{B e^{3+}}=-13.6\left(\frac{ Z ^{2}}{ n ^{2}}\right)$

$=-13.6\left(\frac{4^{2}}{2^{2}}\right)$

$=-54.4 \,e.V$

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