Question

In terms of Bohr radius \(a_0\), the radius of \(2^{nd}\) Bohr orbit of Hydrogen is:

• A. \(4a_0\)
• B. \(8a_0\)
• C. \(\sqrt{2}a_0\)
• D. \(2a_0\)

Hint:

Radius of Bohr orbit: \[ r_n=n^2a_0 \] Thus: \[ r_1=a_0,\qquad r_2=4a_0,\qquad r_3=9a_0 \]

Answer 1

The Correct Option is A

Step 1: Write the formula for Bohr orbit radius.
Radius of \(n^{th}\) Bohr orbit is: \[ r_n=n^2a_0 \] where: \[ a_0=\text{Bohr radius} \]

Step 2: Substitute \(n=2\).
For second orbit: \[ r_2=(2)^2a_0 \] \[ r_2=4a_0 \]

Step 3: Identify the correct option.
Therefore: \[ \boxed{r_2=4a_0} \] Hence, the correct answer is: \[ \boxed{\mathrm{(A)}} \]