The radius of electron's second stationary orbit in Bohr's atom is R . The radius of 3 r d orbit will be

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Question: Answered & Verified by Expert

The radius of electron's second stationary orbit in Bohr's atom is

R

. The radius of

3^{r d}

orbit will be

PhysicsAtomic PhysicsJEE MainJEE Main 2023 (31 Jan Shift 2)

Options:

A $\frac{R}{3}$
B $2.25 R$
C $3 R$
D $9 R$

Solution:

2776 Upvotes Verified Answer

The correct answer is:

2.25 R

As we know, radius of hydrogen like atom $r \propto \frac{n^{2}}{Z}$ .

Therefore,

$\frac{r_{2}}{r_{3}} = {(\frac{n_{2}}{n_{3}})}^{2}$

$\Rightarrow \frac{R}{r_{3}} = {(\frac{2}{3})}^{2}$

$\Rightarrow r_{3} = \frac{9}{4} R$

$= 2.25 R$

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