A radioactive sample has initial concentration `N_(0)` of nuclei. Then,

Options

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 tiem
C. the number of decayed nuclei grows exponentially with time
D. the number of decayed nuclei grows lineraly with time

Answer

a,b

Explanation

We know,
`N=N_(0) e^(- lambda t)`
Where, `N=number` of decayed nuclei in the sample at time t, `N_(0)` =initial number of nuceli.
Hence, total number of undecayed nuclei `=(N_(0)=N)`
Substituing it in (i), we get
`N_(0)-N=N_(0)(1-e^(-lambda t))`
This shows that the total number of undecayed nuclei decays exponentially with time. Now,
`R= -lambda=(dN)/(dt)" "(R=activiy)`
Hence , activityy `(R) rho` number of undecayed nuclei. Therefore, (a), (b),(c) are correct answers.