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Atoms and Nuclei question

2024 · 27 Jan · Shift 1 · Q71

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Atoms and Nuclei
2024 · 27 Jan · Shift 1 · Q71

Atoms and Nuclei question

2024 · 27 Jan · Shift 1 · Q71

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

A
$\frac{4}{3} \mathrm{R}$
B
$\frac{16}{9} R$
C
$\frac{3}{4} R$
D
$\frac{9}{16} \mathrm{R}$

View written solutionFree

Correct answer: B

Use Bohr's radius formula

For a Bohr atom, the radius of the $n^{\text{th}}$ orbit is proportional to $n^2$ : $r_n \propto n^2$

Hence, $\frac{r_4}{r_3} = \frac{4^2}{3^2} = \frac{16}{9}$
Relate given radius

Given that the radius of the third orbit is: $r_3 = R$

Therefore, $r_4 = \frac{16}{9} R$
Match with options

The correct option is: $\boxed{\frac{16}{9}R}$

So, Option B is correct.

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