Question

Assertion :A triply ionized $Be$-atom has the same radius of $2$nd orbit as that of ground state $H$-atom. Reason: The radius of an orbit is $r_n=\frac{r_1\times n^2}{Z}$.

• A. Statement is correct but Explanation is wrong.
• B. Statement is wrong but Explanation is correct.
• C. Both Statement and Explanation are correct and Explanation is the correct explanation for Statement.
• D. Both Statement and Explanation are correct but Explanation is not the correct explanation for Statement.

Answer 1

The correct option is C Both Statement and Explanation are correct and Explanation is the correct explanation for Statement.

The radius of an orbit is given by the expression $r_n=\frac{r_1\times n^2}{Z}$
For triply ionized atom of Be, $Z=4andn=2$.
The expression becomes $r_{2_{B{e}^{3+}}}=\frac{r_1\times 2^2}{4}$
For the ground state of hydrogen atom, $Z=1,n=1$
The expression for the radius becomes $r_{1_H}=\frac{r_1\times 1^2}{1}$
Thus, A triply ionized Be-atom has the same radius of 2nd orbit as that of ground state H-atom.
Hence, both Statement and Explanation are correct and Explanation is the correct explanation for Statement.