Radioactivity
Alpha, β and γ decay, decay law, half-life and mean life. (Physics › Atoms and Nuclei, NEET UG syllabus.)
What is Radioactivity?
The spontaneous process by which an unstable atomic nucleus transforms into a more stable nucleus by emitting particles (α, β) and/or electromagnetic radiation (γ rays).
Key formula / rule: Radioactive Decay Law
Key points
- Define radioactivity and explain its spontaneous nature.
- Describe the characteristics and nuclear changes associated with α, β (β⁻ and β⁺), and γ decay.
- State and apply the radioactive decay law.
- Define and calculate half-life and mean life of a radioactive substance.
Common exam trap
Confusing half-life with mean life or thinking they are the same.
Definitions
- Term
Radioactivity
- Meaning
The spontaneous process by which an unstable atomic nucleus transforms into a more stable nucleus by emitting particles (α, β) and/or electromagnetic radiation (γ rays).
- Term
Decay Constant (λ)
- Meaning
The probability per unit time for a nucleus to decay. It is characteristic of a specific radioisotope.
- Term
Half-life (T₁/₂)
- Meaning
The time required for half of the radioactive nuclei in a given sample to undergo decay.
- Term
Mean Life (τ)
- Meaning
The average lifetime of a radioactive nucleus in a sample. It is the reciprocal of the decay constant.
- Term
Activity (R)
- Meaning
The rate at which radioactive nuclei in a sample decay, measured in decays per unit time. Its SI unit is Becquerel (Bq).
- Term
Alpha Decay
- Meaning
A type of radioactive decay in which an atomic nucleus emits an α particle (helium nucleus, ⁴₂He), reducing its atomic number by 2 and mass number by 4.
- Term
Beta Decay
- Meaning
A type of radioactive decay involving the emission of an electron (β⁻ decay) or a positron (β⁺ decay) from the nucleus, changing the atomic number but not the mass number.
- Term
Gamma Decay
- Meaning
A type of radioactive decay in which an excited atomic nucleus emits a high-energy photon (γ ray) to transition to a lower energy state, without changing its atomic or mass number.
Learning objectives
Define radioactivity and explain its spontaneous nature.
Describe the characteristics and nuclear changes associated with α, β (β⁻ and β⁺), and γ decay.
State and apply the radioactive decay law.
Define and calculate half-life and mean life of a radioactive substance.
Understand the concept of activity and its units.
Solve numerical problems involving decay constant, half-life, mean life, and activity.
Compare the properties (charge, mass, penetration, ionization) of α, β, and γ radiations.
Formulae
- Name
Radioactive Decay Law
- Note
N(t) is number of nuclei at time t, N₀ is initial number, λ is decay constant.
- Expression
N(t) = N₀e^(-λt)
- Name
Half-life
- Note
Time for half of the nuclei to decay.
- Expression
T₁/₂ = ln(2)/λ = 0.693/λ
- Name
Mean Life
- Note
Average lifetime of a radioactive nucleus.
- Expression
τ = 1/λ
- Name
Relationship between Half-life and Mean Life
- Note
Connects the two time constants.
- Expression
T₁/₂ = τ * ln(2) ≈ 0.693τ
- Name
Activity
- Note
Rate of decay, also R(t) = R₀e^(-λt).
- Expression
R = -dN/dt = λN
- Name
Number of nuclei remaining after 'n' half-lives
- Note
Useful for quick calculations over integer half-lives.
- Expression
N = N₀ * (1/2)n, where n = t/T₁/₂
Prerequisites
Basic understanding of atomic structure (protons, neutrons, electrons).
Knowledge of isotopes and isobars.
Concept of nuclear force and nuclear stability.
Basic exponential functions and logarithms.
Common mistakes
Confusing half-life with mean life or thinking they are the same.
Incorrectly applying the decay law, especially with units of time or decay constant.
Forgetting to account for the change in atomic/mass number for different decay types.
Not understanding the role of neutrinos/antineutrinos in β decay.
Mixing up the properties (ionizing/penetrating power) of α, β, γ radiations.
Calculating the remaining fraction instead of the decayed fraction, or vice-versa.
Keywords
Radioactivity
Alpha decay
Beta decay
Gamma decay
Decay constant
Half-life
Mean life
Activity
Becquerel
Curie
Nuclear transformation
Neutrino
Antineutrino
Ionizing power
Penetration power
Practice preview
Which of the following radioactive radiations has the highest penetrating power?…
easy
According to the law of radioactive decay, the activity (A) of a radioactive sample is directly proportional to:…
easy
A radioactive nucleus 238U92 undergoes a series of decays, emitting 8 alpha particles and 6 beta-minus particles. What are the mass number and atomic number of the final daughter nucleus?…
hard