Question

A radioactive nucleus undergoes a series of decay according to the scheme:
\[A\xrightarrow{\alpha }{{A}_{1}}\xrightarrow{\beta }{{A}_{2}}\xrightarrow{\alpha }{{A}_{3}}\xrightarrow{\gamma }{{A}_{4}}\]
If the mass number and atomic number of ‘A’ are 180 and 72 respectively, then the mass number and atomic number for ${{A}_{4}}$ :
A.172 and 69
B. 174 and 70
C. 176 and 69
D. 176 and 70

Answer 1

Hint: Radioactive elements have a particular life, for which they undergo decay and complete their life. The half course that they complete in their life is known as their half life.

Complete answer:
We have been given a reaction sequence, where alpha, beta, and gamma particles are acting on an element. These particles in the sequence, decays the element ‘A’ four times, first the alpha particle acts, then beta particle, then again alpha particle, and at the end gamma particle results in ${{A}_{4}}$.
These particles act on A and subsequently reduce their atomic number and mass number, by the times of the respective mass and atomic numbers of alpha, beta and gamma particles.
Starting from the mass number and atomic number of ‘A’, given as 180 and 72 respectively. We will reduce the mass and atomic numbers of the value of the particles from this value of A.
The mass number and atomic numbers of:
$\alpha $ = 4 and +2
$\beta $ = 0 and -1
$\gamma $ = 0 and 0, respectively. We will reduce these values from the mass and atomic number of A as,
\[\begin{align}
  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A\xrightarrow{\alpha }{{A}_{1}}\xrightarrow{\beta }{{A}_{2}}\xrightarrow{\alpha }{{A}_{3}}\xrightarrow{\gamma }{{A}_{4}} \\
 & mass\,no.\,\,\,\,\,\,180\,\,\,\,\,\,\,\,\,\,\,\,176\,\,\,\,\,\,\,\,\,\,\,\,\,176\,\,\,\,\,\,\,\,\,\,\,\,\,172\,\,\,\,\,\,\,\,\,\,\,\,\,\,172 \\
 & atomic\,no.\,\,\,\,\,72\,\,\,\,\,\,\,\,\,\,\,70\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,71\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,69\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,69 \\
\end{align}\]
So, the atomic number and mass number of ${{A}_{4}}$ is found to be 172 and 69 respectively.

Hence, option A is correct.

Note:
Alpha particle is the helium nucleus so it has a mass of helium which is 4 and atomic number or charge is 2. While a beta particle has a mass of 0 and charge is the same as an electron. While gamma particles are generally gamma waves, so they do not possess any mass or charge.