Question

A radioactive element Y emits an alpha particle and a beta successively and changes into an element ${}_{{\text{82}}}{{\text{X}}^{{\text{206}}}}$. Find the atomic mass and atomic number of radioactive element Y.

Answer 1

Radioactivity is the process where unstable atomic nuclei are converted into stable nuclei with the liberation of energy and particles like positrons, electrons, alpha, or beta particles.
The radioactivity is carried out by using the radiation hence, the type of radiation used determines the types of radioactive decays. The three most common types of radioactive decay are alpha decay, beta decay, and gamma decay.

Complete answer:
Here, it is given that the element Y first emits alpha particles from its nucleus. As the alpha particle is equivalent to a helium nucleus, as it is emitted from the parent element the resulting element has an atomic number less than two units and a mass number less than 4 units as that of the parent element.
$_{\text{M}}{{\text{Y}}^{\text{A}}}{ \to _{{\text{M - 2}}}}{{\text{Z}}^{{\text{A - 4}}}}\,\,{\text{ + }}\,{\,_2}{\text{H}}{{\text{e}}^4}$
Here, the new element is formed by the emission of the beta particle.
$_{\text{M}}{{\text{Y}}^{\text{A}}}{ \to _{{\text{M - 2}}}}{{\text{Z}}^{{\text{A - 4}}}}\,\,{\text{ + }}\,{\,_2}{\text{H}}{{\text{e}}^4} \to {}_{{\text{82}}}{{\text{X}}^{{\text{206}}}} + {{\text{e}}^{{\text{ - 1}}}}$
As the beta particle is emitted the mass number of the newly formed element remains the same but the atomic number is increasing by one unit.
Here, we can see that the newly formed element X possesses mass number 206 hence, the mass number of the Z is the same because X is formed from the Z by the emission of beta particles which does not change the mass number of the Z but its atomic number is changed. The atomic number of the X is 82, which is one unit higher than the atomic number of the Z. Hence, the atomic number of the Z is 81 and its mass number is 206.
Now, Z is formed from the Y by alpha decay which leads to a decrease in the atomic number of the Y by two units and mass number by four units. Here, the atomic number of the Z is 81 and the mass number is 206, therefore, the atomic number of the Y is 83 and the mass number of the Y is 210.

Note: In radioactive decay processes, the particles liberated are alpha, beta particles, and gamma radiation.The alpha particles are consist of two protons and two neutrons hence considered as a helium nucleus.The beta particles are of two types ${\beta ^ + }$ that are positron and ${\beta ^ - }$ that is the electron.The emission of the gamma rays does not change the atomic number and the mass number of the parent element.