Q176 / 180 · KCET 2016 · Physics
An element \( X \) decays into element \( Z \) by two-step process.
\[
\begin{array}{l}
X \rightarrow Y+4 e \\
Y \rightarrow Z+2 e^{-} \text {then }:
\end{array}
\]
\[ \begin{array}{l} X \rightarrow Y+4 e \\ Y \rightarrow Z+2 e^{-} \text {then }: \end{array} \]
- A\( X \& Z \) are isobars.
- B\( X \& Y \) are isotopes
- C\( X \& Z \) are isotones
- Correct answerD\( X \& Z \) are isotopes
Solution
The two processes are as follows:
\[ \mathrm{z}^{\mathrm{A}} X \rightarrow_{\mathrm{Z}-2}^{\mathrm{A}-{ }^{4} Y+{ }_{2}{ }^{4} \mathrm{He}} \]
Since \( X \) and \( Z \) have same atomic number, that is, same number of protons but different atomic mass, that is, sum of
number of protons and neutrons.
We know isotopes are atoms with same number of protons but different number of neutrons. Therefore, \( X \) and \( Z \) are
isotopes.
\[ \mathrm{z}^{\mathrm{A}} X \rightarrow_{\mathrm{Z}-2}^{\mathrm{A}-{ }^{4} Y+{ }_{2}{ }^{4} \mathrm{He}} \]
Since \( X \) and \( Z \) have same atomic number, that is, same number of protons but different atomic mass, that is, sum of
number of protons and neutrons.
We know isotopes are atoms with same number of protons but different number of neutrons. Therefore, \( X \) and \( Z \) are
isotopes.
Hence, the correct answer is option: 'D'.