Q.40 Physics ⭐ 360° Option Elimination Active

NEET 2026 Physics Question 40 Solution

Topic: Atoms & Nuclei · Official NTA Booklet Code 50

Question

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity √25.6 × 10⁵ m s⁻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]

✓

Verified Against NTA Final Answer Key

Option (4) : x = 1 (r = 1 * 10^-9 m)

📚 Atoms & Nuclei Medium

📋 Given Parameters & Problem Setup

Orbital Velocity v = sqrt(25.6) * 10^5 m/s ==> v^2 = 25.6 * 10^10 m^2/s^2

Electron Mass m = 9 * 10^-31 kg

Electron Charge e = 1.6 * 10^-19 C ==> e^2 = 2.56 * 10^-38 C^2

Coulomb Constant 1 / (4*pi*epsilon_0) = 9 * 10^9 N m^2 C^-2

Given Form of Radius r = x * 10^-9 m

Target Variable Value of x

⚡

The 30-Second Exam Hall Shortcut: ⚡ Dynamic Balance Cancellation Trick

⏱️ Bypasses calculating the quantum principal number n.

Centripetal force m*v^2 / r = k*e^2 / r^2 ==> r = k*e^2 / (m*v^2)!

1 Notice the numbers chosen by NTA: k = 9*10^9 and m = 9*10^-31 (The 9s cancel!).

2 e^2 = (1.6*10^-19)^2 = 2.56*10^-38.

3 v^2 = 25.6*10^10.

4 Ratio e^2 / v^2 = (2.56 / 25.6) * (10^-38 / 10^10) = 0.1 * 10^-48 = 10^-49.

5 Combine with (k / m) = (9*10^9) / (9*10^-31) = 10^40.

6 r = (k / m) * (e^2 / v^2) = 10^40 * 10^-49 = 10^-9 m = 1 * 10^-9 m.

7 Therefore, x = 1. Solved in 20 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Newtonian centripetal balance m*v^2/r = k*e^2/r^2 holds exactly for any Bohr orbit. NTA specifically calibrated sqrt(25.6) and m=9 to yield an exact integer 1.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulate Centripetal Force Balance for Electron Orbit

For an electron of mass m moving at speed v in a circular orbit of radius r around a proton (+e):

\frac{m v^2}{r} = \frac{1}{4\pi \epsilon_0} \frac{e^2}{r^2}

• One factor of r cancels from both sides.
• m v^2 r = \frac{1}{4\pi \epsilon_0} e^2.

Step 2

Isolate Orbital Radius r

Rearrange to solve explicitly for orbital radius r:

r = \left( \frac{1}{4\pi \epsilon_0} \right) \frac{e^2}{m v^2}

• Notice that this formula does not even require knowing the principal quantum number n!

Step 3

Substitute Constants and Evaluate x

Substitute the numerical values provided in the question header:

r = \frac{(9 \times 10^9) \times (1.6 \times 10^{-19})^2}{(9 \times 10^{-31}) \times (\sqrt{25.6} \times 10^5)^2} = \frac{(9 \times 10^9) \times (2.56 \times 10^{-38})}{(9 \times 10^{-31}) \times (25.6 \times 10^{10})}

• Cancel 9 from numerator and denominator.
• 2.56 / 25.6 = 0.1 = 10^-1.
• Powers of 10: 10^9 * 10^-38 / (10^-31 * 10^10) = 10^-29 / 10^-21 = 10^-8.
• r = 10^-1 * 10^-8 = 10^-9 m = 1 * 10^-9 m.
• Comparing with r = x * 10^-9 m: x = 1.
• Matches Option (4) exactly.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 Option (1)

✗ Incorrect

Verdict & Scientific Reason:

Used principal quantum number n.

⚠️

Student Fallacy (Why candidates pick this trap): Identifies the state as n = 4 and assumes x = n.

Note: Radius scales as r = n^2 * a_0; radius is 1 nm, not 4 nm.

2 Option (2)

✗ Incorrect

Verdict & Scientific Reason:

Arithmetic error.

⚠️

Student Fallacy (Why candidates pick this trap): Divides 25.6 by 9.

Note: The factor 9 cancels out completely.

3 Option (3)

✗ Incorrect

Verdict & Scientific Reason:

Forgot square in velocity.

⚠️

Student Fallacy (Why candidates pick this trap): Uses v instead of v^2 in the denominator.

Note: Centripetal acceleration is v^2 / r, requiring v^2.

4 Option (4)

✓ 100% Correct

Verdict & Scientific Reason:

100% mathematically exact; confirmed by Official NTA Final Answer Key.

💡

Why this is airtight: Flawless cancellation of coefficients and powers of 10.

Note: Exact physics.

⚠️

NTA Trap Alert: Attempting to Find n First (The Wasted 3-Minute Loop)

Many candidates calculate v = (2.18 * 10^6) / n, square both sides to find n, and then use r = n^2 * 0.529 A, introducing decimal rounding errors.

🛡️ How to avoid the -1 mark: Whenever v and constants are given directly, use r = k*e^2 / (m*v^2) in a single direct step!

📖

Core NEET Syllabus Standard

NEET UG Physics Core Standards · Atoms Standard Benchmark

Core Scientific Principle Tested:

"Dynamic equilibrium of electron in orbit: m*v^2/r = e^2 / (4pi*epsilon_0*r^2). Orbital radius is directly linked to orbital speed by r = e^2 / (4pi*epsilon_0*m*v^2)."

Syllabus Focus: Bohr Model of Hydrogen Atom: Orbital Velocity and Radius

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 180-minute timed NTA simulator.

Launch NEET 2026 CBT Test →

← Previous (Q.39) All Physics Questions Grid Next (Q.41) →

🔗 Related Questions — Atoms & Nuclei

All 2 Atoms & Nuclei PYQs →

NEET 2026 Q35

Geiger-Marsden Experiment: Scattered Alpha Particles vs Scattering Angle Plot

View Solution →

Spotted a mistake in this solution? Report an error (support@mycompetitiveexams.com)

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2026 question papers and NEET answer keys for private study, research, and non-commercial educational practice under Fair Dealing (Section 52(1)(a) of the Indian Copyright Act, 1957). Not affiliated with or endorsed by NTA or NMC.

NEET 2026 Physics Question 40 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Dynamic Balance Cancellation Trick

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulate Centripetal Force Balance for Electron Orbit

Isolate Orbital Radius r

Substitute Constants and Evaluate x

360° Option Elimination Engine Key Feature

NTA Trap Alert: Attempting to Find n First (The Wasted 3-Minute Loop)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Atoms & Nuclei

Geiger-Marsden Experiment: Scattered Alpha Particles vs Scattering Angle Plot

Solve 4 NEET Questions a Day — One per Subject