Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEET 2026
Exam
NEET
Year
2026
Subject
Chemistry
Chapter
Chapter

NEET 2026 · Chemistry · Chapter

What are the energy of the second Bohr orbit of Be^ 3+ and the...

What are the energy of the second Bohr orbit of Be3+\mathrm{Be}^{3+} and the radius of the third Bohr orbit of He+\mathrm{He}^{+} respectively?
[Given: RH=2.18×10−18 J,a0=52.9 pm\mathrm{R}_{\mathrm{H}} = 2.18 \times 10^{-18} \text{ J}, \mathrm{a}_0 = 52.9 \text{ pm}]

Options

  1. A−8.72×10−18 J-8.72 \times 10^{-18} \text{ J} and 238.05 pm238.05 \text{ pm}
  2. B−2.18×10−18 J-2.18 \times 10^{-18} \text{ J} and 79.35 pm79.35 \text{ pm}
  3. C−4.36×10−18 J-4.36 \times 10^{-18} \text{ J} and 119.03 pm119.03 \text{ pm}
  4. D−8.72×10−18 J-8.72 \times 10^{-18} \text{ J} and 79.35 pm79.35 \text{ pm}

Correct answer

A. −8.72×10−18 J-8.72 \times 10^{-18} \text{ J} and 238.05 pm238.05 \text{ pm}

Step-by-step solution

The energy of the nn-th Bohr orbit for a hydrogen-like species is given by En=−RH×Z2n2E_n = -R_H \times \dfrac{Z^2}{n^2}

For Be3+\mathrm{Be}^{3+}, the atomic number Z=4Z = 4. For the second orbit, n=2n = 2.

E2=−2.18×10−18×4222=−2.18×10−18×4=−8.72×10−18 JE_2 = -2.18 \times 10^{-18} \times \dfrac{4^2}{2^2} = -2.18 \times 10^{-18} \times 4 = -8.72 \times 10^{-18} \text{ J}

The radius of the nn-th Bohr orbit is given by rn=a0×n2Zr_n = a_0 \times \dfrac{n^2}{Z}

For He+\mathrm{He}^{+}, the atomic number Z=2Z = 2. For the third orbit, n=3n = 3.

r3=52.9×322=52.9×4.5=238.05 pmr_3 = 52.9 \times \dfrac{3^2}{2} = 52.9 \times 4.5 = 238.05 \text{ pm}

Answer: −8.72×10−18 J-8.72 \times 10^{-18} \text{ J} and 238.05 pm238.05 \text{ pm}
Practice Chapter on Quantrex Academy →

More from Chapter

Which of the following postulates of Dalton's atomic theory provides the direct… NEET 2026Consider the following five samples of substances: A. 88 g of CO_2 B. 96 g of O_2 C. 34 g… NEET 2026If the shortest wavelength of the Lyman series for a hydrogen atom is x , then the… NEET 2026Consider the following electronic configurations of neutral atoms: A. [Ne] 3s^2 3p^4 B.… NEET 2026Consider the following sequences of molecules and their associated properties: (I) CH_3Cl… NEET 2026The potential energy profile for a hypothetical reaction X arrow Y is shown in the given… NEET 2026For a reversible gas-phase reaction, X(g) + Y(g) leftharpoons Z(g) the rate constant for… NEET 2026Consider the following equilibrium for the synthesis of sulfur trioxide: 2SO_2(g) +… NEET 2026 Full Chapter list All NEET PYQs