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RE-NEET2026Physics-Atomic Structure

RE-NEET 2026 Physics Bohr Model MCQ Question

Type: MCQ-numerical-Medium-Class 11

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity √25.6 ×10⁵ ms⁻¹. The radius of the orbit is x×10⁻⁹ m. The value of x is: [Take the mass of electron to be 9×10⁻³¹ kg, charge of electron = −1.6×10⁻¹⁹ C and 1/4πε₀ = 9×10⁹ N m² C⁻²]

A

3

B

2

C

1

D

4

Correct Answer

Option C

Detailed Explanation

To find the radius of the orbit of an electron in a hydrogen atom, we use the formula for the radius in the Bohr model:

r=n2⋅h24π2⋅m⋅k⋅e2r = \frac{n^2 \cdot h^2}{4 \pi^2 \cdot m \cdot k \cdot e^2}

where k=14πϵ0k = \frac{1}{4 \pi \epsilon_0}. Given the velocity v=25.6×105 m/sv = \sqrt{25.6 \times 10^5} \, \text{m/s}, we can find the corresponding radius using the centripetal force balance with electrostatic force.

After calculations, we find rr to be 1×10−9 m1 \times 10^{-9} \, \text{m}, leading to x=1x = 1.

The other options fail because they do not satisfy the derived relationship for the radius based on the given parameters.

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