Chapter 24, Problem 89A

Interpretation Introduction

Interpretation:

Decay series of thorium-231 to lead-207 with successive emissions of $\text{β, α, α, β, α, α, α, β, β, α}$ is to be plotted on graph as mass number versus atomic mass.

Concept introduction:

In a nuclear reaction, unstable nuclide disintegrates into stable nuclide with emission of various radiations spontaneously. It is called radioactivity of nucleus. Emission of rays like alpha, beta and gamma rays occur in the process which changes the identity of nucleus.

During a nuclear change, an element undergoes change in its atomic mass or atomic number or both by emission of charged particles such as beta particle, alpha particle. Beta particle is one that has unit negative charge and alpha particle is one that has 2 unit positive charges and is equivalent to helium atom ${}_2^4\text{He}$. Emission of proton, beta particle, alpha particle causes a change in atomic number of element.

Answer to Problem 89A

Decay series of thorium-231 to lead-207 with successive emissions of $\text{β, α, α, β, α, α, α, β, β, α}$ is presented as follows:

Explanation of Solution

$\text{β}$ decay leads to increase in atomic number by 1 unit and mass number remains same whereas $\text{α}$ decay leads to decrease in atomic number by 2 unit and mass number by 4 unit.

Decay series of thorium-231 to lead-207 with successive emissions of $\text{β, α, α, β, α, α, α, β, β, α}$ is presented as follows:

In above image, A is $\text{β}$ decay, B is the $\text{α}$ decay, C is the $\text{α}$ decay, D is the $\text{β}$ decay, E is the $\text{α}$ decay, F is the $\text{α}$ decay, G is the $\text{α}$ decay, H is the $\text{β}$ decay, I is the $\text{β}$ decay and J is the $\text{α}$ decay.

The plot of mass number versus atomic mass for the same is as follows:

The labels A, B, C, D, E, F, G, H, I and J represent the steps of decay reaction defined above.

Conclusion

Decay series of thorium-231 to lead-207 with successive emissions of $\text{β, α, α, β, α, α, α, β, β, α}$ is presented as follows: