Question

The ratio of radii of second orbit of hydrogen atom to fourth orbit of \(He^+\) ion is:

• A. \(1:4\)
• B. \(2:1\)
• C. \(1:2\)
• D. \(2:3\)

Hint:

For hydrogen-like species, \[ r_n=\frac{n^2a_0}{Z} \] Thus, orbital radius is directly proportional to \(n^2\) and inversely proportional to the atomic number \(Z\).

Answer 1

The Correct Option is C

Step 1: Write the Bohr radius formula.
For a hydrogen-like atom, \(r_n = rac{n^2 a_0}{Z}\), where \(Z\) is atomic number.

Step 2: Compute each radius as a ratio.
H (n=2, Z=1): \(r \propto rac{4}{1} = 4\). He\(^+\) (n=4, Z=2): \(r \propto rac{16}{2} = 8\). Ratio = \(4:8 = 1:2\). \[ oxed{1:2} \]