If the radius of second Bohrs orbit of hydrogen atom is a0 then the radius of third Bohrs orbit of Be3+ ion will be:
Correct answer: A. 9/16a0
- A. 9/16a0
- B. 3a0
- C. 1.5a0
- D. 4a0
Explanation
Step 1: Bohr's radius formulaFor the nth orbit of a hydrogen-like ion:rₙ = (n² × a₀) / ZWhere:n = orbit number (principal quantum number)a₀ = Bohr radius of hydrogen atom's first orbitZ = atomic number of the nucleusStep 2: Given dataRadius of second Bohr's orbit of hydrogen = a₀We need: Radius of third Bohr's orbit of Be³⁺ ionZ for Be³⁺ = 4 (beryllium's atomic number)Step 3: Find a₀ in terms of given hydrogen orbitFor hydrogen (Z = 1),r₂ = (2² × a₀) / 1 = 4 a₀But the question says radius of second orbit of hydrogen is a₀,so here a₀ (in question) is actually 4 × (Bohr constant a₀ actual).Let's call Bohr's actual constant a₀(real).Given:4 × a₀(real) = a₀ (given in question)So, a₀(real) = a₀(given) / 4Step 4: Radius for Be³⁺, n = 3r₃(Be³⁺) = (3² × a₀(real)) / Z= (9 × (a₀(given) / 4)) / 4= (9 a₀(given)) / 16
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