First slide

Radio activity

Question

The fraction f of radioactive material that has decayed in time t, varies with time t. The correct variation is given by the curve

Moderate

A

A
B

B
C

C
D

D

Solution

Number of atoms undecayed $N = N_{0} e^{- λt}$
Number of atoms decayed $= N_{0} - N = N_{0} (1 - e^{- λt})$
$\Rightarrow$ Decayed fraction $f = \frac{N_{0} - N}{N_{0}} = 1 - e^{- λt}$
i.e., fraction will rise up to 1, following exponential path as shown in graph (B).

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