Question

In a radioactive decay chain, \[Th_{90}^{232}\]nucleus decays to \[Pb_{82}^{212}\]nucleus. Let \[{{N}_{\alpha }}\]and \[{{N}_{\beta }}\]be the number of \[\alpha \And \beta \]particles respectively, emitted in this decay process. Which of the following statements are/is true?
A. \[{{N}_{\beta }}=2\]
B. \[{{N}_{\alpha }}=6\]
C. \[{{N}_{\alpha }}=5\]
D. \[{{N}_{\alpha }}=6\]

Answer 1

Hint: Radioactivity refers to the phenomenon in which the substance decays by emission of radiation. Half-life is defined as the time taken by the material in which the number of undecayed atoms becomes half. A material containing unstable nuclei is considered radioactive.

Complete step by step answer:
\[Th_{90}^{232}\] gets converted to \[Pb_{82}^{212}\]
The difference in mass number is 232-212= 20
The difference in atomic number is 90-82= 8
We know alpha particles have mass number 4 and atomic number 2 and beta particles have mass number 0 and atomic number -1.
No of alpha particles= \[\dfrac{20}{4}=5\]
Since, each alpha has atomic number 2, so, 10 must be the change in atomic number but we are getting it 8. Thus, number of beta particles is 10-8= 2
So, the number of alpha particles is 5 and the number of beta particles are 2.

So, the correct answers are “Option A and C”.

Additional Information:
Half-life is the time for half the radioactive nuclei in any sample to undergo radioactive decay. For example, after 2 half-lives, there will be one fourth the original material remains, after three half-lives one eight the original material remains, and so on. Half-life is a convenient way to assess the rapidity of a decay

Note:
Alpha particles are doubly ionized helium nuclei, so they are positively charged and beta particles are fast moving electrons, so they are negatively charged. Both alpha particles and beta particles get deflected in the presence of electric and magnetic fields.