Question

A radioactive nuclide is produced at the constant rate of n per second (say, by bombarding a target with neutrons). The expected number N of nuclei in existence t seconds after the number is N_0­is given by –

• A. N = N₀e^–lt
• B. N = $\frac{n}{\lambda}$ + N₀e^–lt
• C. N = $\frac{n}{\lambda}$ + $\left( N_{0}–\frac{n}{\lambda} \right)$ e^–lt
• D. N = $\frac{n}{\lambda}$ + $\left( N_{0} + \frac{n}{\lambda} \right)$ e^–lt

Answer 1

Answer: (C)

N = $\frac{n}{\lambda}$ + $\left( N_{0}–\frac{n}{\lambda} \right)$ e^–lt

Answer 2

Method 1 Method 2

$\frac { \mathrm { dN } } { \mathrm { dt } }$= n – lN At t = 0

= N = N₀

$\frac { 1 } { \lambda }$log_e $\left( \frac { \mathrm { n } - \lambda \mathrm { N } _ { 0 } } { \mathrm { n } - \lambda \mathrm { N } } \right)$ = t Which is satisfied

N = $\frac { \mathrm { n } } { \lambda }$ + e^–lt by (3) only