Question

Half-life of ${}^{24}Na$ is $900$ minutes. What is its decay constant?

Answer 1

Hint: Half-life and decay constant are the terms which are associated with radioactive decay. Radioactive decay can be defined as the process in which an unstable nucleus loses energy in the form of radiation. We will now see the terms half-life and decay constant and then calculate the decay constant using a formula.

Complete answer:
Radioactive decay can be defined as the process in which an unstable nucleus loses energy in the form of radiation.
We can define the half-life of a radioactive isotope as time required to degrade one-half of the substance into a more stable substance during a radioactive dacay. Half-life is represented as ${t_{\dfrac{1}{2}}}$ .
Decay constant is basically the proportionality between the population of radioactive atoms and the rate of decreasing population due to radioactive decay. It is represented as $\lambda .$
We can find the decay constant by using the formula as follows:
$\lambda = \dfrac{{0.693}}{{{t_{\dfrac{1}{2}}}}}$
${t_{\dfrac{1}{2}}} = 900$
Put the value of half-life in the formula above to find out the decay constant:
$\lambda = \dfrac{{0.693}}{{900}}$
$\lambda = 7.7 \times {10^{ - 4}}{\min ^{ - 1}}$
Here, the unit of decay constant is ${\min ^{ - 1}}$ because the value of half-life has minutes as its unit.
Therefore, the decay constant of ${}^{24}Na$ is found to be $7.7 \times {10^{ - 4}}{\min ^{ - 1}}.$

Note:
We should remember that half-life is that time period in which the concentration of a radioactive substance decreases to half of the initial concentration after a radioactive decay and decay constant can be understood as the proportionality between the population of radioactive atoms and the rate of decreasing population due to radioactive decay.