Reason for difficulty in detecting presence of antineutrino during $\beta$ decay Define decay constant of radioactive nucleus Derive expression for mean life in terms of decay constant ● Penetrating power is high ● Do not interact with matter (weak interaction) (any one) ● Decay constant is the reciprocal of the time duration in which undecayed radioactive nuclei reduce to $\frac{1}{e}$ times the nuclei present initially. $\tau = \frac{\text{total life time of all nuclei}}{\text{total number of nuclei}}$$\tau = \frac{\int\limits_{0}^{\infty} t dN}{N_0}$$\tau = \frac{\int\limits_{0}^{\infty} t \left( N_0 \lambda \varepsilon^{- \lambda t} dt \right)}{N_0} = \lambda \int t e^{- \lambda t} dt$$\tau = \frac{1}{\lambda}$ OR (a) Stating distinguishing feature of nuclear force. (b) Drawing a plot showing variation of potential energy. (c) Marking the regions. (1) Short rang force (2) Strongest force (3) Attractive in nature (4) Does not depend on charge (any two) (b) $r < r_0$ : repulsive force$r > r_0:$ attractive force