Derive the relationship between half life and decay constant of a…

Question

Derive the relationship between half life and decay constant of a radioelement.

✓

Answer

Equation for the decay constant is given as,
$
\lambda=\frac{2.303}{t} \log _{10} \frac{ N _0}{ N } \text {...(i) }
$
Where, $\lambda=$ Decay constant
$N =$ Number of nuclei (atoms) present at time $t$
At $t =0, N = N _0$.
Hence, at $t=t_{1 / 2}, N=N_0 / 2$
Substitution of these values of $N$ and $t$ in equation (i) gives,
$
\begin{aligned}
\lambda & =\frac{2.303}{t_{1 / 2}} \log _{10} \frac{N_0}{\frac{N_0}{2}} \\
& =\frac{2.303}{ t _{1 / 2}} \log _{10} 2=\frac{2.303}{ t _{1 / 2}} \times 0.3010=\frac{0.693}{ t _{1 / 2}}
\end{aligned}
$
Hence, $\lambda=\frac{0.693}{t_{1 / 2}}$ or $t _{1 / 2}=\frac{0.693}{\lambda}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following questions." from Nuclear Chemistry and Radioactivity→Nuclear Chemistry and Radioactivity — all question types→Chemistry STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Nuclear Chemistry and Radioactivity — Chemistry STD 11 Science — Question

Answer

Need a full question paper?

Explore more

Similar questions