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Module 8: From the Universe to the Atom
Quick questions on Radioactive decay and half-life: HSC Physics Module 8
14short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is what radioactive decay is?Show answer
A radioactive nucleus is one that spontaneously transforms into another nuclear state, releasing energy as kinetic energy of the products and/or as electromagnetic radiation. Decay is a random process for any individual nucleus, but the statistics for large samples follow a predictable exponential law. The probability per unit time that a given nucleus decays is the decay constant $\lambda$, independent of how long the nucleus has existed.
What is alpha decay?Show answer
A heavy nucleus emits an alpha particle ($^4_2$He, two protons and two neutrons). The atomic number decreases by 2, mass number by 4.
What is beta-minus decay?Show answer
A neutron in the nucleus converts to a proton, emitting an electron (the beta particle) and an electron antineutrino. Atomic number increases by 1, mass number unchanged.
What is beta-plus decay?Show answer
A proton in the nucleus converts to a neutron, emitting a positron and an electron neutrino. Atomic number decreases by 1, mass number unchanged.
What is gamma decay?Show answer
The nucleus is left in an excited state after an alpha or beta decay (or after a nuclear reaction). It drops to a lower state by emitting a high-energy photon (gamma ray). No change in $Z$ or $A$.
What is balancing nuclear equations?Show answer
In any decay equation, two conservation laws must hold:
What is the decay law?Show answer
If $N(t)$ is the number of undecayed nuclei at time $t$, the rate of decay is proportional to $N$:
What is half-life?Show answer
The half-life $T_{1/2}$ is the time for half the sample to decay. From $N(T_{1/2}) = N_0 / 2$:
What is worked example?Show answer
A wooden bowl contains $^{14}$C at 25% of the modern atmospheric ratio. The half-life is 5730 y. Estimate the age.
What is forgetting the antineutrino in beta decay?Show answer
Charge balances without it, but lepton number does not. Always include $\bar{\nu}_e$ for beta-minus and $\nu_e$ for beta-plus.
What is confusing $\lambda$ and $T_{1/2}$?Show answer
They are related by $\lambda T_{1/2} = \ln 2$, not $\lambda T_{1/2} = 1$. The numerical factor matters.
What is using arithmetic decay instead of exponential?Show answer
Each half-life removes half the remaining sample, not half the initial sample. After two half-lives the sample is 25% of the original, not 0%.
What is confusing $A$ and $Z$ in alpha decay?Show answer
Alpha decay reduces $A$ by 4 and $Z$ by 2. Both must change together.
What is saying gamma decay changes the element?Show answer
Gamma decay changes the nuclear excitation level only. The element is unchanged.