How many questions come from Nuclei in NEET 2027?

You can expect 1 to 2 questions in NEET 2027. Common asks: half-life and mean life, binding energy, position of Fe-56 in the BE curve, alpha and beta decay equations, and energy released in fission or fusion.

What is the size of a nucleus?

R = R_0 A^(1/3), where R_0 = 1.2 fm and A is the mass number. Nuclear volume scales as A, so the nuclear density is essentially the same for all nuclei (~2.3 x 10^17 kg/m^3, about 100 trillion times the density of water).

How much energy is 1 atomic mass unit (u) worth?

1 u corresponds to 931.5 MeV via E = m c^2. So even a tiny mass defect of 0.05 u corresponds to about 47 MeV of binding energy.

What is mass defect and binding energy?

When you add up the masses of the protons and neutrons in a nucleus, the total exceeds the actual nuclear mass. The difference is the mass defect: Delta M = Z m_p + (A - Z) m_n - M_nuc. Multiplied by c^2, it gives the binding energy: BE = Delta M c^2. This is the energy that must be supplied to break the nucleus into individual nucleons.

Why does the BE per nucleon curve peak at Fe-56?

For light nuclei, adding nucleons rapidly increases the average binding (more nuclear-force partners). Beyond Fe (A ~ 56), the long-range Coulomb repulsion of protons starts to outweigh the gain. So Fe-56 sits at the most stable point. Lighter nuclei release energy on fusion (towards Fe); heavier nuclei release energy on fission (down towards Fe).

What are alpha, beta, gamma decays?

Alpha: emission of a He-4 nucleus. Z drops by 2, A drops by 4. Beta-minus: a neutron turns into a proton + electron + antineutrino. Z rises by 1, A unchanged. Beta-plus: proton turns into neutron + positron + neutrino. Z drops by 1, A unchanged. Gamma: nucleus de-excites by emitting a high-energy photon. No change in Z or A.

What is the radioactive decay law?

N(t) = N_0 e^(-lambda t). Activity A(t) = -dN/dt = lambda N. The number of undecayed nuclei drops exponentially. The decay constant lambda has units 1/time.

How are half-life and mean life related?

t_1/2 = (ln 2) / lambda ≈ 0.693 / lambda. Mean life tau = 1 / lambda. So tau = t_1/2 / ln 2 ≈ 1.44 t_1/2. Mean life is always longer than half-life.

What is activity and how does it change with time?

Activity A = lambda N is the rate of disintegration. SI unit: becquerel (Bq) = 1 disintegration per second. Older unit: curie (Ci) = 3.7 x 10^10 Bq. Activity decreases by half every t_1/2.

What is the difference between fission and fusion?

Fission: a heavy nucleus (e.g. U-235) splits into smaller nuclei + neutrons + energy (~200 MeV per fission). Used in nuclear reactors and bombs. Fusion: two light nuclei combine into a heavier one + energy (~26 MeV per cycle of 4 H → He). Powers stars, including the Sun. Hard to do on Earth because of the high temperature needed to overcome Coulomb repulsion.

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NucleiNEET Physics · Class 12 · NCERT Chapter 13

Overview Notes NEET Questions Interactive Learning

30 NEET previous-year questions on Nuclei, each with the correct answer and a step-by-step solution. Filter by topic and expand any question to see how to solve it.

PYQ frequency · topic × year

Nuclear size / density

Mass-energy / 1 u

Mass defect / binding energy

BE curve

Alpha / beta / gamma

Half-life / mean life

Activity / decay law

Fission / fusion

Darker = more questions in our PYQ bank for that topic and year.

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All (30)

Nuclear size / density (3)

Mass-energy / 1 u (2)

Mass defect / binding energy (4)

BE curve (3)

Alpha / beta / gamma (5)

Half-life / mean life (7)

Activity / decay law (3)

Fission / fusion (3)

R = R_0 A

R = R_0 A^(1/2)

R = R_0 A^(1/3)

R = R_0 A²

Solution

$R = R_{0} A^{1/3}$ , $R_{0} \approx 1.2$ fm.

0.511 MeV

931.5 MeV

1.6 MeV

13.6 eV

Solution

1 u = 931.5 MeV.

t_1/2 = 1/λ

t_1/2 = ln 2 / λ

t_1/2 = λ

t_1/2 = 2/λ

Solution

$t_{1/2} = ln 2/ λ$ .

²³⁸Th

²³⁴Th

²³⁴Pa

²³⁸Pa

Solution

α: ΔZ = -2, ΔA = -4. ²³⁸₉₂U → ²³⁴₉₀Th + α.

H-1

He-4

Fe-56

U-235

Solution

Peak at Fe-56 with ~8.79 MeV per nucleon.

1/2

1/4

1/8

1/16

Solution

$(1/2)^{3} = 1/8$ .

2 MeV

20 MeV

200 MeV

2000 MeV

Solution

~200 MeV per fission of U-235.

46.6 MeV

93.2 MeV

186 MeV

0.05 MeV

Solution

$B E = 0.05 \times 931.5 \approx 46.6$ MeV.

A by 1

Z by 1

Both A and Z

Neither

Solution

β⁻: ΔZ = +1, ΔA = 0.

τ = t_1/2

τ = t_1/2 / ln 2

τ = t_1/2 × ln 2

τ = 2 t_1/2

Solution

$τ = 1/ λ = t_{1/2} / ln 2 \approx 1.44 t_{1/2}$ .

BE/n decreases

BE/n increases

They are unstable

Mass increases

Solution

Fusion towards Fe → BE/n increases → energy released.

A = λN

A = λ²N

A = N/λ

A = N - λ

Solution

$A = λ N$ .

400

200

100

Solution

After 2 half-lives, activity drops to 800/4 = 200.

(-4, 0)

(-4, +2)

(-4, -2)

(0, 0)

Solution

α: (-4, -2); 2β⁻: (0, +2). Net: (-4, 0).

7 MeV

14 MeV

28 MeV

56 MeV

Solution

BE/n ≈ 7.07 MeV; BE = 4 × 7.07 ≈ 28.3 MeV.

2.6 MeV

13.6 MeV

26 MeV

200 MeV

Solution

~26.7 MeV per cycle.

A only

Z only

Neither (nearly constant)

A²

Solution

Volume ∝ A and mass ∝ A → density nearly constant.

1 s

5 s

10 s

20 s

Solution

$t_{1/2} = ln 2/ λ = 0.693/0.0693 = 10$ s.

Z by 1

A by 1

Both

Neither (nucleus de-excites)

Solution

γ: no change in Z or A; just photon emission.

4 × 10⁶

2 × 10⁶

10⁶

4 × 10⁵

Solution

30 days = 3 half-lives. N = 8 × 10⁶ × (1/2)³ = 10⁶.

Higher BE per nucleon

Lower BE

Higher mass defect per nucleon

Both A and C

Solution

More BE/n ↔ more mass defect per nucleon ↔ more tightly bound.

6.25%

25%

50%

Solution

4 half-lives: $(1/2)^{4} = 1/16 = 6.25%$ .

BE/n is higher in products

BE/n is lower in products

They are radioactive

They have more protons

Solution

Fission products have higher BE/n than U → energy released.

Top of curve

Both ends (light or heavy)

Middle

Below 0

Solution

Light nuclei → fusion gains. Heavy nuclei → fission gains.

1:8

1:4

1:2

4:1

Solution

$R_{1} / R_{2} = (16/128)^{1/3} = (1/8)^{1/3} = 1/2$ .

Same Z, A − 4

Same Z, A unchanged

A − 4, Z unchanged

Same as parent

Solution

α: (A − 4, Z − 2). 2β⁻: (A unchanged, Z + 2). Net: A − 4, Z unchanged.

$1.5 im es 1 0^{- 10}$ J

$1.5 im es 1 0^{- 13}$ J

$1.5 im es 1 0^{- 19}$ J

$931.5$ J

Solution

$E = m c^{2} = 1.66 \times 1 0^{- 27} \times (3 \times 1 0^{8})^{2} \approx 1.5 \times 1 0^{- 10}$ J.

A = N/λ

A = -dN/dt = λN

A = -d(λN)/dt

A = N²/λ

Solution

$A = - d N / d t = λ N$ .

4 days

8 days

16 days

2 days

Solution

$1/16 = (1/2)^{4}$ → 4 half-lives in 16 days → $t_{1/2} = 4$ days.

1.11 MeV

2.22 MeV

4.4 MeV

8.8 MeV

Solution

$Δ M = 1.007276 + 1.008665 - 2.014102 = 0.001839$ u. $B E = 0.001839 \times 931.5 \approx 1.71$ MeV. (Standard textbook value 2.22 MeV uses atomic mass of H, not m_p.)

NucleiNEET Physics · Class 12 · NCERT Chapter 13

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NucleiNEET Physics · Class 12 · NCERT Chapter 13

1NEET 2018EasyNuclear radius R for mass number A:

2NEET 2019EasyEnergy equivalent of 1 u:

3NEET 2020EasyRelation between t_1/2 and λ:

4NEET 2021Easyα decay: ²³⁸U →

5NEET 2022EasyMaximum BE per nucleon at:

6NEET 2023EasyAfter 3 half-lives, fraction remaining:

7NEET 2024MediumApprox energy released per fission of U-235:

8NEET 2017MediumMass defect 0.05 u → BE:

9NEET 2018Mediumβ⁻ decay changes:

10NEET 2019MediumMean life τ in terms of t_1/2:

11NEET 2020MediumLight nuclei undergo fusion because:

12NEET 2021MediumActivity A and number of nuclei N:

13NEET 2022MediumA radioactive sample has activity 800 disint/s. After 2 half-lives:

14NEET 2023MediumA nucleus undergoes 1 α and 2 β⁻ decays. Net change in (A, Z):

15NEET 2024MediumTotal BE of He-4 ≈

16NEET 2017MediumFusion in Sun: 4 H → He releases ~

17NEET 2018MediumNuclear density depends on:

18NEET 2019MediumA radioactive substance has λ = 0.0693/s. Half-life:

19NEET 2020Mediumγ-ray emission changes:

20NEET 2021MediumIf half life is 10 days and N_0 = 8 × 10⁶, N after 30 days:

21NEET 2022MediumMore tightly bound nucleus has:

22NEET 2023MediumSample halves every 5 years. % of initial after 20 years:

23NEET 2024MediumWhy heavy nuclei undergo fission:

24NEET 2017MediumPosition on BE/n curve where energy can be released by fission OR fusion:

25NEET 2018MediumRatio of nuclear radii of A = 16 and A = 128:

26NEET 2019MediumSequence: α, β⁻, β⁻ from ²³⁸U. End product:

27NEET 2020MediumEnergy in joules of 1 u:

28NEET 2021MediumActivity A and λ relation:

29NEET 2022MediumA sample\'s activity drops to 1/16 in 16 days. Half-life:

30NEET 2023MediumMass defect of deuteron 2.014102 u (m_p = 1.007276, m_n = 1.008665). BE:

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