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NEET 2026
Exam
NEET
Year
2026
Subject
Physics
Chapter
Chapter

NEET 2026 · Physics · Chapter

If the radius of the second Bohr orbit of a singly ionized helium...

If the radius of the second Bohr orbit of a singly ionized helium atom (He+He^+) is xx, then the radius of the third Bohr orbit of a doubly ionized lithium atom (Li2+Li^{2+}) will be:

Options

  1. A94x\dfrac{9}{4}x
  2. B32x\dfrac{3}{2}x
  3. Cxx
  4. D23x\dfrac{2}{3}x

Correct answer

B. 32x\dfrac{3}{2}x

Step-by-step solution

The radius of the nn-th Bohr orbit for a hydrogen-like species is given by rn∝n2Zr_n \propto \dfrac{n^2}{Z}.

For the second Bohr orbit of He+He^+ (n=2n = 2, Z=2Z = 2):
x∝222⇒x∝2x \propto \dfrac{2^2}{2} \Rightarrow x \propto 2

For the third Bohr orbit of Li2+Li^{2+} (n=3n = 3, Z=3Z = 3):
r∝323⇒r∝3r \propto \dfrac{3^2}{3} \Rightarrow r \propto 3

Taking the ratio of the two radii:
rx=32\dfrac{r}{x} = \dfrac{3}{2}

r=32xr = \dfrac{3}{2}x

Answer: 32x\dfrac{3}{2}x
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