Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Calculate the specific activities of
nuclides whose half lives are 15 hours and
years respectively.
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Identify the half-lives of the nuclides: Na\textsuperscript{24} has a half-life of 15 hours and U\textsuperscript{235} has a half-life of approximately 703.8 million years (or 1.11114 x 10^9 hours).
Step 2: Use the formula for specific activity (A) which is given by:
A = \frac{N\lambda}{M}
where N is the number of radioactive nuclei, \lambda is the decay constant, and M is the molar mass.
For Na\textsuperscript{24}:
The decay constant \lambda = \frac{\ln{2}}{T_{1/2}} = \frac{0.693}{54000 \text{ seconds}} = 1.285\times 10^{-5} \text{ s}^{-1}.
The specific activity is calculated in Bq/g. M = 24 g/mol for Na\textsuperscript{24}.
Similarly, for U\textsuperscript{235}:
The decay constant \lambda = \frac{0.693}{703800000 \text{ hours}} = 1.14 \times 10^{-9} \text{ hours}^{-1} = 3.17 \times 10^{-10} \text{ s}^{-1}.
The molar mass M = 235 g/mol for U\textsuperscript{235}.
Therefore, specific activity calculations yield values which can be compared directly to find the result.
Step 2: Use the formula for specific activity (A) which is given by:
A = \frac{N\lambda}{M}
where N is the number of radioactive nuclei, \lambda is the decay constant, and M is the molar mass.
For Na\textsuperscript{24}:
The decay constant \lambda = \frac{\ln{2}}{T_{1/2}} = \frac{0.693}{54000 \text{ seconds}} = 1.285\times 10^{-5} \text{ s}^{-1}.
The specific activity is calculated in Bq/g. M = 24 g/mol for Na\textsuperscript{24}.
Similarly, for U\textsuperscript{235}:
The decay constant \lambda = \frac{0.693}{703800000 \text{ hours}} = 1.14 \times 10^{-9} \text{ hours}^{-1} = 3.17 \times 10^{-10} \text{ s}^{-1}.
The molar mass M = 235 g/mol for U\textsuperscript{235}.
Therefore, specific activity calculations yield values which can be compared directly to find the result.
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