If a radioactive substance decays for time interval equal to its mean life; then its fraction that remains undecayed will be

The mean life of a radioactive substance, denoted by T, is defined as the average time it takes for half of the radioactive nuclei in a sample to decay. It is related to the decay constant (λ) by the equation:

$T = \frac{1}{ \lambda }$

where λ is the decay constant.

We are given that the time interval for decay is equal to the mean life of the substance, which means that the time (t) for which the substance decays is equal to T.

We can use the formula for radioactive decay:

Fraction of remaining undecayed nuclei = $e^{\mathbf{(}\mathbf{-}\mathit{\lambda }\mathit{t}\mathbf{)}}$

Substituting t = T:

Fraction of remaining undecayed nuclei = $e^{\mathbf{(}\mathbf{-}\mathit{\lambda }\mathit{T}\mathbf{)}}$

Since $T = \frac{1}{ \lambda }$, we can substitute this into the equation:

Fraction of remaining undecayed nuclei = $e^{-1}$

Using the value of the base of natural logarithm (e ≈ 2.71828), we can calculate:

Fraction of remaining undecayed nuclei ≈ 0.3678794412

Hence the correct answer is 0.36.