Question

One of the lines in the emission spectrum of Li²+ has the same wavelength as that of the 2nd line of the Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is n = 12 → n = x. Find the value of x.

• A. \(8\)
• B. \(6\)
• C. \(7\)
• D. 5

Hint:

For hydrogen-like ions, wavelength scales as 1/Z².

Answer 1

The Correct Option is D

Step 1: Rydberg formula: (1)/(λ) = RZ²((1)/(n₁²)-(1)/(n₂²))
Step 2: For hydrogen Balmer 2nd line: (1)/(λ) = R((1)/(2²)-(1)/(4²))
Step 3: For Li²+: R(3²)((1)/(x²)-(1)/(12²))
Step 4: Equating gives x = 5.