C
CraftExam
medium difficulty9 min

Radioactivity: Alpha, Beta and Gamma Decay

Radioactivity is the spontaneous transformation of an unstable nucleus with emission of alpha particles, beta particles, or gamma radiation. The number of undecayed nuclei follows N = N0 e^(-λ t), and half-life is T1/2 = ln 2/λ.

In one line: Alpha changes A and Z; beta changes Z; gamma changes energy only.

Concept Practice Coming Soon

Understand it

  • Radioactive decay is a nuclear process and is not controlled by ordinary chemical conditions.
  • In alpha decay, the nucleus emits a helium nucleus, so A decreases by 4 and Z decreases by 2.
  • In beta-minus decay, a neutron changes into a proton with emission of an electron and an antineutrino, so Z increases by 1 while A remains the same.
  • In beta-plus decay, a proton changes into a neutron with emission of a positron and a neutrino, so Z decreases by 1 while A remains the same.
  • Gamma emission releases excess nuclear energy without changing A or Z.

Example

If a radioactive sample has half-life 5 days, then after 10 days, two half-lives have passed. The remaining fraction is (1/2)2 = 1/4 of the original undecayed nuclei.

Formula and rule

N = N0 e^(-λ t), where N is undecayed nuclei after time t, N0 is initial undecayed nuclei, λ is decay constant in s−1, and t is time in second.

Activity Aactivity = λ N, with SI unit becquerel.

T1/2 = ln 2/λ.

Use exponential law for continuous decay and half-life fractions for integer numbers of half-lives.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A sample has 8.0 × 106 undecayed nuclei and half-life 4 h.

  1. 1Find nuclei left after 12 h.
  2. 2Number of half-lives = 12/4 = 3.
  3. 3Remaining nuclei = 8.0 × 106 × (1/2)3 = 1.0 × 106.
  4. 4So 1.0 × 106 undecayed nuclei remain.

Method you can reuse

  1. 1For decay equations, conserve mass number and atomic number.
  2. 2For half-life numericals, calculate n = t/T1/2 and use N = N0(1/2)n when n is simple.
  3. 3For exponential questions, use N = N0 e^(-λ t).
  4. 4For activity, use Aactivity = λ N.

Visual tip

A decay curve should have time on the x-axis and number of undecayed nuclei or activity on the y-axis. It falls exponentially and never reaches zero in finite time. For decay equations, labels should show parent nucleus, emitted particle, daughter nucleus, and changes in A and Z.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What remains of a radioactive sample after three half-lives?

Think first, then show answer
After three half-lives, the remaining undecayed fraction is (1/2)3 = 1/8 of the original sample.

Common wrong answer

A common wrong answer is changing mass number during beta decay. In beta decay, atomic number changes by one, but mass number remains unchanged.

Don't mix this up

Students often think half-life means the whole sample disappears after two half-lives. Actually, after each half-life, half of the remaining undecayed nuclei are left.

Exam tip

For alpha and beta decay, write changes in A and Z before naming the daughter nucleus. For half-life numericals, count the number of half-lives using t/T1/2.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

This concept appears as decay equation balancing, half-life numericals, activity relation, decay graph interpretation, and comparison of alpha, beta, and gamma radiation.
  1. 1

    Enough for 1 mark

    Radioactivity is the spontaneous transformation of an unstable nucleus with emission of alpha particles, beta particles, or gamma radiation. The number of undecayed nuclei follows N = N0 e^(-λ t), and half-life is T1/2 = ln 2/λ.

  2. 2

    Add for 2 marks

    Example: If a radioactive sample has half-life 5 days, then after 10 days, two half-lives have passed. The remaining fraction is (1/2)2 = 1/4 of the original undecayed nuclei.

  3. 3

    Add for 3 marks

    Radioactive decay is a nuclear process and is not controlled by ordinary chemical conditions.

Practice

Concept practice is coming soon

Login to access concept-level MCQs and weak-concept practice as they become available.

10 MCQs5 MinutesInstant Results
Login

Help improve this page

Found something confusing, incorrect, or missing?

Open Learning Map