Atoms And Nuclei Question 378

Question: One gram of a radioactive sample of half-life 10 min is sealed in a capsule at time t=0. Amount of sample decayed up to 5 min is

Options:

A) 0.293g

B) 0.5g

C) 0.25g

D) 0.707g

Show Answer

Answer:

Correct Answer: A

Solution:

  • Use the relation $ N=N_{0}{{e}^{-\lambda t}} $ where the decay constant

    $ \lambda =(0.693/T_{half}). $ The half-life period

    $ T_{half} $ is given to be 10min.

    The amount N of radioactive sample remaining at the end of 5 min comes out to be about $ 0.707g, $

    so that the amount of sample decayed is $ (1-0.707)=0.293g. $



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