Question

From data presented in the first few paragraphs of Module 42-3, find (a) the disintegration constant $\mathit{\lambda }$and (b) the half-life of 238U

Short answer

(a) The disintegration constant of U-238 is .

(b) The half-life of the U-238 is .

Step-by-step solution

Radioactive decay

Radioactive decay is the process of decaying protons from the nucleus and variation in the mass number of the atom. The number of protons increases by one unit due to beta decay and no change in the mass number of the atom, while the number of protons changes by two units and mass number by four units for alpha decay.

Determination of half-life of U-238(b)

The duration in which the amount of any radioactive substance becomes half of its initial amount is called the half-life of that substance. The amount of uranium is 238 halves in $4.6\times {10}^{9}y$.

Therefore, the half-life of the U-238 is $4.6\times {10}^{9}y$.

Determination of disintegration constant(a)

The disintegration constant of U-238 is calculated as:

$\mathrm{\lambda }=\frac{\mathrm{In}2}{{\mathrm{t}}_{1/2}}$

Substitute all the values in the above equation.

$$\begin{gathered} \lambda =\frac{\mathrm{In}2}{\left(4.6\times {10}^9\mathrm{y}\right)\left({\displaystyle \frac{3.154\times {10}^7\mathrm{s}}{1\mathrm{y}}}\right)} \\ =4.8\times {10}^{-18}{\mathrm{s}}^{-1} \end{gathered}$$

Therefore, the disintegration constant of U-238 is $4.8\times {10}^{-18}{s}^{-1}$.