Question

Radius of the first excited state of Helium ion is given as:
\(a_0\) = radius of first stationary state of hydrogen atom.

• A. \( r = \frac{a_0}{2} \)
• B. \( r = \frac{a_0}{4} \)
• C. \( r = 4a_0 \)
• D. \( r = 2a_0 \)

Hint:

To find the radius of the excited state of an atom or ion, use the formula \( r = \frac{a_0 n^2}{Z} \), where \( a_0 \) is the Bohr radius.

Answer 1

The Correct Option is D

The radius of the first excited state of the Helium ion is given by the formula: \[ r = \frac{a_0 n^2}{Z} \] where \( a_0 \) is the Bohr radius, \( n \) is the principal quantum number, and \( Z \) is the atomic number. For the first excited state of the He\(^+\) ion, \( n = 2 \) and \( Z = 2 \). Thus: \[ r = a_0 \left(\frac{2^2}{2}\right) = 2a_0 \] Thus, the correct answer is \( \boxed{2a_0} \).