Radioactive decay
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What experimental evidence supports the random nature of radioactive decay?
Fluctuations in count rate over short periods provide evidence. The count rate varies even when measuring the same radioactive source due to the unpredictable nature of individual decay events.
Distinguish between 'spontaneous' and 'random' in the context of radioactive decay.
'Spontaneous' means decay is not influenced by external factors (temperature, pressure). 'Random' means that it is impossible to predict when a specific nucleus will decay; only probabilities can be stated.
Define 'activity' (A) of a radioactive source.
Activity (A) is the rate at which nuclei decay in a radioactive source. It is measured in Becquerels (Bq), where 1 Bq = 1 decay per second.
Define the 'decay constant' (λ).
The decay constant (λ) is the probability of decay of a nucleus per unit time. It is related to the activity and number of undecayed nuclei by A = λN.
State the relationship between activity (A), decay constant (λ), and number of undecayed nuclei (N).
The relationship is given by the equation: A = λN, where A is activity, λ is the decay constant, and N is the number of undecayed nuclei.
Define 'half-life' (t₁/₂).
Half-life (t₁/₂) is the time taken for half of the radioactive nuclei in a sample to decay, or the time taken for the activity of a sample to decrease to half its initial value.
State the relationship between half-life (t₁/₂) and decay constant (λ).
The relationship is given by the equation: λ = 0.693 / t₁/₂, where λ is the decay constant and t₁/₂ is the half-life.
Describe the exponential nature of radioactive decay using an equation.
The number of undecayed nuclei (N) at time t is given by: N = N₀e^(-λt), where N₀ is the initial number of nuclei and λ is the decay constant. Similar equations apply for activity and count rate.
A radioactive sample has an initial activity of 400 Bq and a half-life of 10 days. What is its activity after 30 days?
After 30 days (3 half-lives), the activity is reduced by half three times: 400 Bq -> 200 Bq -> 100 Bq -> 50 Bq. Therefore, the activity after 30 days is 50 Bq.
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