Give the different units of radioactivity and define them. 

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The SI unit for activity is Becquerel $(\mathrm{B} q)$ named after the discoverer of radioactivity,

Henry Becquerel.

$(i)$ Activity of a substance having 1 disintegration per second is called 1 Becquerel (B $q$ ). $\therefore 1 \mathrm{~B} q=1$ decay/s

$(ii)$ Curie unit : The activity of a substance in which $3.7 \times 10^{10}$ disintegration per second take place is called l curie $(\mathrm{C} i)$.

$\therefore 1 \mathrm{Ci}=3.7 \times 10^{10}$ decay/s

In practice its smaller units are used,

$1 \mathrm{mC} i=3.7 \times 10^{7}$ decay/s $=10^{-3} \mathrm{Ci}$

$1 \mu \mathrm{C} i=3.7 \times 10^{4}$ decay/s $=10^{-6} \mathrm{C} i$

Curie unit is the old experimental unit.

(iii) Rutherford unit : It is defined as the activity of a quantity of radioactive substance in which $10^{6}$ (ten lakh) nuclei decay per second is called Rutherford $(\mathrm{rd})$. $\therefore 1 \mathrm{rd}=10^{6}$ decay/s

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A sample initially contains only $U -238$ isotope of uranium. With time, some of the $U -238$ radioactively decays into $Pb -206$ while the rest of it remains undisintegrated.

When the age of the sample is $P \times 10^8$ years, the ratio of mass of $Pb -206$ to that of $U -238$ in the sample is found to be $7$ . The value of $P$ is. . . . . .

[Given : Half-life of $U-238$ is $4.5 \times 10^9$ years; $\log _e 2=0.693$ ]

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