JEE Main 2025 Apr 2 Shift 1, Chemistry Q5: Bohr's Atomic Model

JEE Main2025Apr 2, Shift 1Chemistry

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

A
Radius of $3^{r d}$ orbit is nine times larger than that of $1^{s t}$ orbit.
B
Radius of $8^{t h}$ orbit is four times larger than that of $4^{t h}$ orbit.
C
Radius of $6^{t h}$ orbit is three time larger than that of $4^{t h}$ orbit.
D
Radius of $4^{t h}$ orbit is four times larger than that of $2^{n d}$ orbit.

Solution

For Bohr's hydrogen atom the orbital radius scales as $r_{n} \propto n^{2}$ , so the ratio between two orbits is $\frac{r _{a}}{r _{b}} = (\frac{a}{b})^{2}$ .

Checking each option:

(1) $\frac{r _{3}}{r _{1}} = \frac{9}{1} = 9$ $\Rightarrow$ statement true.

(2) $\frac{r _{8}}{r _{4}} = \frac{64}{16} = 4$ $\Rightarrow$ statement true.

(3) $\frac{r _{6}}{r _{4}} = \frac{36}{16} = \frac{9}{4} = 2.25$ , not 3 $\Rightarrow$ statement false.

(4) $\frac{r _{4}}{r _{2}} = \frac{16}{4} = 4$ $\Rightarrow$ statement true.

$∴$ The incorrect statement is option (3).

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JEE Main 2025 Apr 2 Shift 1, Chemistry Q5: Bohr's Atomic Model

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