Atoms & Nuclei

JEE Main level, single correct, medium

55 of 239

Question 55 of 239

The radius of electron's second stationary orbit in Bohr's atom is RR. The radius of 3rd{3}^{rd} orbit will be

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Answer: (B) 2.25R2.25R

As we know, radius of hydrogen like atom r∝n2Zr\propto \dfrac{{n}^{2}}{Z}.
Therefore,

r2r3=(n2n3)2\dfrac{{r}_{2}}{{r}_{3}}={\left(\dfrac{{n}_{2}}{{n}_{3}}\right)}^{2}
⇒Rr3=(23)2\Rightarrow \dfrac{R}{{r}_{3}}={\left(\dfrac{2}{3}\right)}^{2}
⇒r3=94R\Rightarrow {r}_{3}=\dfrac{9}{4}R
=2.25R=2.25R

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