JEE Main · 2020 · Shift-IIeasyATOM-058

The radius of the second Bohr orbit, in terms of the Bohr radius a0, in Li2+ is:

Structure of Atom · Class 11 · JEE Main Previous Year Question

Question

The radius of the second Bohr orbit, in terms of the Bohr radius a0a_0, in Li2+\mathrm{Li^{2+}} is:

Options
  1. a

    2a03\frac{2a_0}{3}

  2. b

    4a09\frac{4a_0}{9}

  3. c

    4a03\frac{4a_0}{3}

  4. d

    2a09\frac{2a_0}{9}

Correct Answerc

4a03\frac{4a_0}{3}

Detailed Solution

🧠 The Fundamental Unit Scaling We need the radius of the 2nd Bohr orbit for \ceLi2+\ce{Li^2+}. In JEE, this is often asked "in terms of a0a_0" so we don't need to plug in 0.5290.529. Just manage nn and ZZ.

🗺️ The Variable Mapping

  1. Formula: rn=n2a0Zr_n = \frac{n^2 a_0}{Z}.
  2. Ion: Lithium (Z=3Z=3).
  3. State: 2nd orbit (n=2n=2).
  4. Result: r2=22a03=4a03r_2 = \frac{2^2 a_0}{3} = \frac{4 a_0}{3}

The "Squares and Atomic Numbers" Mental Table

  • H, n=1 \to a0a_0
  • He+, n=1 \to a0/2a_0/2
  • Li2+, n=2 \to 4/3a04/3 a_0 Being able to visualize this simple table of n2/Zn^2/Z factors makes these questions trivial.

⚠️ Common Traps Wait—did you use n=2n=2 or n2n^2? Squaring is the most missed step. 2/3a02/3 a_0 is a common distractor option (Option A). Always double check the power of nn!

Answer: (c)\boxed{\text{Answer: (c)}}

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