A vessel contains 4 × 10^ 23 tritium atoms. Given that the half-life for the decay of tritium nuclei is 12.3 y , determine the activity of the sample.

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Quantrex Academy · Accepted Answer

Correct answer: A. 7.146 × 10^ 14 disintegrations s^ -1

The activity of a radioactive sample is given by the formula:

A = \lambda N

where

\lambda

is the decay constant and

N

is the number of atoms.

The decay constant

\lambda

is related to the half-life

T_{1/2}

by:

\lambda = \dfrac{\ln 2}{T_{1/2}} \approx \dfrac{0.693}{T_{1/2}}

Given:

T_{1/2} = 12.3 \text{ y} = 12.3 \times 365 \times 24 \times 3600 \text{ s} = 3.879 \times 10^8 \text{ s}

N = 4 \times 10^{23}

Substituting these values into the activity formula:

A = \dfrac{0.693}{3.879 \times 10^8} \times 4 \times 10^{23}

A \approx 1.786 \times 10^{-9} \times 4 \times 10^{23}

A \approx 7.146 \times 10^{14} \text{ disintegrations s}^{-1}

A vessel contains 4 × 10^ 23 tritium atoms. Given that the...

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