Question

A radioactive sample has initial concentration $N_0$ of nuclei. Then

• A. the number of undecayed nuclei present in the sample decays exponentially with time
• B. the activity (R) of the sample at any instant is directly proportional to the number of undecayed nuclei present in the sample at that time
• C. the number of decayed nuclei growth exponentially with time
• D. the number of decayed nuclei grows linearly with time

Answer 1

Answer: (A), (B), (C)

the activity (R) of the sample at any instant is directly proportional to the number of undecayed nuclei present in the sample at that time
the number of undecayed nuclei present in the sample decays exponentially with time
the number of decayed nuclei growth exponentially with time

From law of radio activity, $N=N_0{e}^{-\lambda t}$. This equation indicates option B and C will be right.

Activity $=|\frac{dN}{dt}|=N\lambda$. It indicates the option B will be right.