Modern Physics Ques 128
- The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^{-9}$ $ s$. The mass of an atom of this radioisotope is $10^{-25} $ $kg$. The mass (in $mg$ ) of the radioactive sample is
(2011)
Show Answer
Answer:
Correct Answer: 128.$(1)$
Solution:
Formula:
- Activity $(-\frac{d N}{d t})=\lambda N=(\frac{1}{t _{\text {mean }}}) \times N$
$\therefore \quad N=(-\frac{d N}{d t}) \times t _{\text {mean }}=$ Total number of atoms
Mass of one atom is $10^{-25}$ $ kg=m$ (say)
$\therefore \quad$ Total mass of radioactive substance
$ \begin{aligned} & =(\text { number of atoms }) \times(\text { mass of one atom }) \\ & =(-\frac{d N}{d t})\left(t _{\text {mean }}\right)(m) \end{aligned} $
Substituting the values, we get
Total mass of radioactive substance $=1$ $ mg$
$\therefore \quad $ Answer is $1$ .
BETA
