Why is it difficult to detect the presence of an anti-neutrino during \beta -decay ? Define the term decay constant of a radioactive nucleus and derive the expression for its mean life in terms of the decay constant.

 

Answers (1)
S safeer

Since penetrating power is high during \beta - decay, that's the reason for the difficulty in detecting the presence of anti-neutrino.

It also doesn't interact with matter.

The decay constant of a radioactive nucleus is defined as the reciprocal of the time duration in which undecayed radioactive nuclei reduce to 1/e times the nuclei present initially.

In terms of the decay constant, the expression for the mean life.

\tau =\frac{total\; life\; time\; of\; all\; nuclei}{total\; number\; of\; nuclei}

\tau =\frac{\int_{o}^{\infty }tdN}{N_O}

\tau =\frac{\int_{o}^{\infty } t (No\lambda \varepsilon ^{-\lambda t}dt)}{N_0}

\tau =\lambda \int_{0}^{\infty} te^{-\lambda t }dt

\tau =\frac{1}{\lambda }

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