The energy level diagram for a hydrogen like atom is shown in the figure. The radius of its first Bohr orbit is -

0.265 ˚ A

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0.537 ˚ A

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0.132 ˚ A

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None of these

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Solution

The correct option is A $0.265 ˚ A$

We know that,

$E_{n} = - 13.6 \frac{Z^{2}}{n^{2}} eV$

For $n = 1$ ,

$- 54.4 = - 13.6 \frac{Z^{2}}{1^{2}}$

$\Rightarrow Z = 2$

Also,

$r_{n} = 0.53 \frac{n^{2}}{Z} ˚ A$

$\Rightarrow r_{1} = 0.53 \times \frac{1^{2}}{2} = 0.265 ˚ A$

Hence, option $(A)$ is the correct answer.

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The energy level diagram for a hydrogen like atom is shown in the figure. The radius of its first Bohr orbit is -

The correct option is A 0.265 ˚A We know that, En=−13.6Z2n2 eV For n=1, −54.4=−13.6Z212 ⇒Z=2 Also, rn=0.53n2Z ˚A ⇒r1=0.53×122=0.265 ˚A Hence, option (A) is the correct answer.