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# Define the Terms (I) Half-life (T1/2) and (Ii) Average Life (τ). Find Out Their Relationships with the Decay Constant (λ). - Physics

ConceptMass-energy and Nuclear Binding Energy Nuclear Binding Energy

#### Question

Define the terms (i) half-life (T1/2) and (ii) average life (τ). Find out their relationships with the decay constant (λ).

#### Solution

Half-life
The half-life of a radioactive substance is defined as the average time for which the nuclei of the atoms of the radioactive substance exist.

t = t_(1/2)

R =1/2R_0

∴ t_(1/2)=(1n2)/λ

=(0.693)/4

Average life or mean-life (τ):

tau=(λN_0int_0^oo te^(-λ1)dt)/N_0

= λint_0^oo te^(-λ1)dt

tau=1/lambda

∴ T_(1/2)=(1n2)/λ = tau 1n2

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Solution Define the Terms (I) Half-life (T1/2) and (Ii) Average Life (τ). Find Out Their Relationships with the Decay Constant (λ). Concept: Mass-energy and Nuclear Binding Energy - Nuclear Binding Energy.
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