PiTheory

PiTheory JEE Physics Practice & Revision Pack · Class 12 · Chapter 13 · JEE Main

Nuclei

Chapter-wise practice and revision for JEE Main: concise notes on nuclear size and density, mass defect and binding energy, fission and fusion, and radioactive decay, concept figures, and 49 selected previous-year JEE Main questions covering the major concepts and question patterns, each with a step-by-step solution.

49 selected questions4 topics2 concept figuresPreview · first 3 of 49 questions

How to study this chapter

  1. Look at the topic's figures, then read its notes (5 to 10 minutes). They give the major equations and methods the questions use.
  2. Solve the topic's questions with a timer: 2 minutes for Easy, 3 to 4 for Medium and Hard.
  3. Check the solution. Read the Point to note line even if you were right: it is the idea you will reuse.
  4. Mark each question Got it or Revise. Come back to the Revise list after two days.

Where the marks come from

Main idea of each of the 118 previous-year JEE questions in the PiTheory bank

Radioactivity52
Binding energy29
Size, density20
Fission, fusion17

Contents

  1. 1Nuclear size and densityQ1–Q8
  2. 2Mass defect and binding energyQ9–Q20
  3. 3Fission and fusionQ21–Q29
  4. 4Radioactive decayQ30–Q49
  5. ✓Last-day checklist
01

Topic 1 · Q1–Q8

Nuclear size and density

20 of the 118 JEE PYQs in the bank test this as their main idea

Quick notes

$$R=R_0A^{1/3}\ (R_0\approx1.2\text{ fm}),\qquad V\propto A,\qquad \rho=\frac{3m_N}{4\pi R_0^3}\approx2\times10^{17}\ \text{kg/m}^3$$

Nuclear density is the same for all nuclei. Nuclear force: strongest force, short range ($\sim$ fm), charge independent, saturates.

  • $R\propto A^{1/3}$, area $\propto A^{2/3}$.
  • Nucleus at rest splitting in two: equal momenta, so $\dfrac{v_1}{v_2}=\dfrac{m_2}{m_1}$ and $\dfrac{R_1}{R_2}=\left(\dfrac{m_1}{m_2}\right)^{1/3}$.
  • Isotopes: same $Z$; isobars: same $A$; isotones: same $N$.
Trap. Absorbed electrons do not change $A$.

Practice: first 3 of 8 questions

Q1JEE Main 2026 (28 Jan, Shift 2)Easy

A nucleus has mass number $\alpha$ and radius $R_\alpha$. Another nucleus has mass number $\beta$ and radius $R_\beta$.

If $\beta = 8\alpha$ then $R_\alpha/R_\beta$ is :

  1. A1
  2. B2
  3. C8
  4. D0.5
Answer and solution

Answer: Option D: 0.5

Concept. $R=R_0A^{1/3}$.

Step 1. Ratio. $\dfrac{R_\alpha}{R_\beta}=\left(\dfrac{\alpha}{8\alpha}\right)^{1/3}=\dfrac12$.

Answer. $0.5$ (Option D).

Point to note. $R\propto A^{1/3}$.

Q2JEE Main 2024 (1 Feb, Shift 1)Easy

The radius of a nucleus of mass number 64 is $4.8$ fermi. Then the mass number of another nucleus having radius of $4$ fermi is $\dfrac{1000}{x}$, where $x$ is ______.

Numerical answer type

Answer and solution

Answer: 27

Concept. $A\propto R^3$.

Step 1. New mass number. $A=64\left(\dfrac{4}{4.8}\right)^3=64\times\dfrac{125}{216}=\dfrac{1000}{27}$.

Answer. $x=27$.

Point to note. $A\propto R^3$.

Q3JEE Main 2024 (31 Jan, Shift 2)Easy

The mass number of the nucleus having radius equal to half of the radius of the nucleus with mass number 192 is:

  1. A$24$
  2. B$32$
  3. C$40$
  4. D$20$
Answer and solution

Answer: Option A: $24$

Concept. Half the radius means one-eighth of $A$.

Step 1. Value. $\dfrac{192}{8}=24$.

Answer. Option A.

Point to note. $1/8$ of $A$.

46 more questions and 3 more topics in the full chapter

  1. 2Mass defect and binding energy12 questions with solutions
  2. 3Fission and fusion9 questions with solutions
  3. 4Radioactive decay20 questions with solutions
  4. ✓Last-day checklist

The complete Nuclei chapter is in the Class 12 Pack and the Complete Pack, as a PDF on WhatsApp. Want to see a whole chapter first? Laws of Motion and Current Electricity are free in full.

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