Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of Li⁺⁺ ion in its ground state is given by 1/X a₀, where X= __________ (Where a₀ is the first Bohr's radius.)

Solution

Physics sir · 4 steps

Radius goes as n²/Z: lithium has Z = 3 and the ground state has n = 1, so the orbit shrinks threefold.

1. Bohr radius formula. For a hydrogen-like ion with nuclear charge Z, the radius of the nth orbit is set by n² in the numerator and Z in the denominator.

   rₙ = n²/Z a₀

2. Identify n and Z. Lithium has atomic number 3, so Z = 3. Li²⁺ has only one electron left, so the Bohr model applies. Ground state means n = 1.
3. Put in numbers. r₁ = 1²/3 a₀ = 1/3 a₀. A nucleus with three times the charge pulls the single electron three times closer.
4. So. Comparing with 1/Xa₀ gives X = 3, which is option (d).

The idea to keep. In hydrogen-like ions, radius goes as n²/Z, energy as Z²/n² and speed as Z/n. Square only the quantity the formula squares.

Answer from the NTA final answer key. Solution by PrepWiser.