Question

If radius of second Bohr orbit of the He⁺ ion is 105.8pm, What is the radius of third Bohr Orbit of Li²⁺ ion?

• A. 158.7 pm
• B. 15.87 pm
• C. 1.587 pm
• D. 158.7 Å

Answer 1

The Correct Option is A

To solve the problem, we need to determine the radius of the third Bohr orbit of the Li²⁺ ion. Let's start with the known formula for the radius of the n^th Bohr orbit: \(r_n = \frac {n^2 × a_0}{Z}\),
where a₀ is the Bohr radius (approximately 52.9 pm), n is the principal quantum number, and Z is the atomic number of the ion.

Given:

• Radius of second Bohr orbit of He⁺ (Z = 2): 105.8 pm.
• n = 2 for He⁺.

Formula for radius:

For He⁺, \(r_n = \frac {n^2 × a_0}{Z}\)

\(105.8 = \frac {2^2 × a_0}{2}\)

\(105.8 = 2 × a_0\)

Solving for a₀:

• \(a_0 = \frac {105.8}{2} = 52.9\) pm

Now, calculate the radius for the third Bohr orbit of Li²⁺:

• Z = 3 for Li²⁺, n = 3

Formula: \(r_n = \frac {n^2 × a_0}{Z}\)

\(r_3 = \frac {(3^2) × 52.9}{3}\)

\(r_3 =\frac{ (9) × 52.9}{3}\)

\(r_3 = 158.7\) pm

Thus, the radius of the third Bohr orbit of Li²⁺ ion is 158.7 pm.