JEE Main 2023 — Physics Modern Physics

2023integereasy

The radius of ${2}^{\mathrm{nd}}$ orbit of ${\mathrm{He}}^{+}$ of Bohr's model is ${r}_{1}$ and that of fourth orbit of ${\mathrm{Be}}^{3+}$ is represented as ${r}_{2}.$ Now the ratio $\frac{{r}_{2}}{{r}_{1}}$ is $x:1.$ The value of $x$ is _____.

Official previous-year question

Held on 13 Apr 2023 · Verified 6 Jul 2026.

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Solution

The formula to calculate the radius $(r)$ of any ${n}^{\mathrm{th}}$ Bohr's orbit is given by

$r={r}_{0}\frac{{n}^{2}}{Z}...(1)$

where, ${r}_{0}$ is Bohr's radius, $n$ is the principal quantum number and $Z$ is the atomic number.

Thus, for Helium ion,

$\begin{matrix}{r}_{1} & = & {r}_{0}\frac{{2}^{2}}{2} \\ & = & 2{r}_{0}...(2)\end{matrix}$

And, for the Beryllium ion,

$\begin{matrix}{r}_{2} & = & {r}_{0}\frac{{4}^{2}}{4} \\ & = & 4{r}_{0}...(3)\end{matrix}$

Divide equation (3) by equation (2) to obtain the required ratio.

$\begin{matrix}\frac{{r}_{2}}{{r}_{1}} & = & \frac{4{r}_{0}}{2{r}_{0}} \\ & = & 2\end{matrix}$

Hence, $x=2$ .

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JEE Main 2023 — Physics Modern Physics

2023integereasy

Official previous-year question

Held on 13 Apr 2023 · Verified 6 Jul 2026.

Did you get this right?

Solution

The formula to calculate the radius $(r)$ of any ${n}^{\mathrm{th}}$ Bohr's orbit is given by

$r={r}_{0}\frac{{n}^{2}}{Z}...(1)$

where, ${r}_{0}$ is Bohr's radius, $n$ is the principal quantum number and $Z$ is the atomic number.

Thus, for Helium ion,

$\begin{matrix}{r}_{1} & = & {r}_{0}\frac{{2}^{2}}{2} \\ & = & 2{r}_{0}...(2)\end{matrix}$

And, for the Beryllium ion,

$\begin{matrix}{r}_{2} & = & {r}_{0}\frac{{4}^{2}}{4} \\ & = & 4{r}_{0}...(3)\end{matrix}$

Divide equation (3) by equation (2) to obtain the required ratio.

$\begin{matrix}\frac{{r}_{2}}{{r}_{1}} & = & \frac{4{r}_{0}}{2{r}_{0}} \\ & = & 2\end{matrix}$

Hence, $x=2$ .

Your note

JEE Main Modern Physics in other years

Keep practicing Modern Physics

Work through every JEE Main Modern Physics PYQ, year by year.

Browse all Physics topics

JEE Main 2023 — Physics Modern Physics

Did you get this right?

Solution

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JEE Main Modern Physics in other years

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Mechanics

Electromagnetism

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Thermodynamics

Waves & Oscillations

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JEE Main 2023 — Physics Modern Physics

Did you get this right?

Solution

Your note

JEE Main Modern Physics in other years

More JEE Main Modern Physics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Modern Physics