Chemistry Q52 – JEE-MAIN 2025

Home Chemistry Structure of AtomQuestion #618

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

Clue 1 of 3: Bohr's Model Postulates

Recall the formula for the radius of an electron's orbit in Bohr's model for a hydrogen-like atom.

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Ninja Strategy•Bohr's Radius Proportionality

Quickly check each option using the proportionality $r_{n} \propto n^{2}$ to find the statement that does not hold true.

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● Video Walkthrough

Step 1: Recall Bohr's Radius Formula✦ Active

According to Bohr's model, the radius of the $n^{t h}$ orbit for a hydrogen-like atom is given by the formula:

r_{n} = r_{0} \frac{n^{2}}{Z}

For a hydrogen atom, the atomic number $Z = 1$ . Therefore, the radius of an orbit is directly proportional to the square of the principal quantum number $n$ :

r_{n} \propto n^{2}

Step 2: Evaluate Each Statement○ Expand

We will check each option by calculating the ratio of the radii based on the $n^{2}$ proportionality:

1. **Option 1:** Radius of $4^{t h}$ orbit vs $2^{n d}$ orbit. $r_{4} / r_{2} = (4^{2}) / (2^{2}) = 16 / 4 = 4$ . So, $r_{4} = 4 r_{2}$ . This statement is **correct**.

2. **Option 2:** Radius of $6^{t h}$ orbit vs $4^{t h}$ orbit. $r_{6} / r_{4} = (6^{2}) / (4^{2}) = 36 / 16 = 9 / 4 = 2.25$ . This statement claims $r_{6} = 3 r_{4}$ , which is **incorrect**.

3. **Option 3:** Radius of $8^{t h}$ orbit vs $4^{t h}$ orbit. $r_{8} / r_{4} = (8^{2}) / (4^{2}) = 64 / 16 = 4$ . So, $r_{8} = 4 r_{4}$ . This statement is **correct**.

4. **Option 4:** Radius of $3^{r d}$ orbit vs $1^{s t}$ orbit. $r_{3} / r_{1} = (3^{2}) / (1^{2}) = 9 / 1 = 9$ . So, $r_{3} = 9 r_{1}$ . This statement is **correct**.

💡 Teacher's Secret Hint

Pay close attention to the 'incorrect' keyword in the question.

Step 3: Identify the Incorrect Statement○ Expand

Based on the evaluation, the statement that 'Radius of $6^{t h}$ orbit is three times larger than that of $4^{t h}$ orbit' is incorrect, as the actual ratio is 2.25 times.

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Chemistry Question 52 – JEE-MAIN 2025

Clue 1 of 3: Bohr's Model Postulates

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