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The mass numbers of two elements $X$ and $Z$ are 52 and 75 respectively. $X$ contains $16.6 \%$ more neutrons compared to protons. $Z$ contains $27.3 \%$ more neutrons compared to protons. $X$ and $Z$ are respectively
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Verified Answer
The correct answer is:
${ }_{24} \mathrm{Cr}_{{ }_{33}} \mathrm{As}$
Given, mass number of $X=52$
Mass number of $Z=75$
Suppose, number of protons in $X=a$
$\therefore$ Number of neutrons $=0.166 a+a=1.166 a$
As we know that,
Mass number $=$ Number of proton
+ Number of neutron
$$
\begin{aligned}
\therefore 52 & =a+1.166 a \\
52 & =2.166 a \\
a & =24
\end{aligned}
$$
Thus, the element $X={ }_{24} \mathrm{Cr}$
$[\because$ atomic number $=$ number of protons or electrons]
Similarity, for the element $Z$,
$$
\begin{aligned}
75 & =b+1.273 b=2.273 b \\
b & =32.9 \approx 33
\end{aligned}
$$
Thus, the element $Z$ is ${ }_{33}$ As.
Mass number of $Z=75$
Suppose, number of protons in $X=a$
$\therefore$ Number of neutrons $=0.166 a+a=1.166 a$
As we know that,
Mass number $=$ Number of proton
+ Number of neutron
$$
\begin{aligned}
\therefore 52 & =a+1.166 a \\
52 & =2.166 a \\
a & =24
\end{aligned}
$$
Thus, the element $X={ }_{24} \mathrm{Cr}$
$[\because$ atomic number $=$ number of protons or electrons]
Similarity, for the element $Z$,
$$
\begin{aligned}
75 & =b+1.273 b=2.273 b \\
b & =32.9 \approx 33
\end{aligned}
$$
Thus, the element $Z$ is ${ }_{33}$ As.
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