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MCQEasyJEE 2024Bohr Model & Hydrogen Spectrum

JEE Chemistry 2024 Question with Solution

Given below are two statements: Statement-I: The orbitals having the same energy are called as degenerate orbitals. Statement-II: In hydrogen atom, 3p3p and 3d3d orbitals are not degenerate orbitals.

Choose the most appropriate answer from the options below:

  • A

    Statement-I is true but Statement-II is false

  • B

    Both Statement-I and Statement-II are true

  • C

    Both Statement-I and Statement-II are false

  • D

    Statement-I is false but Statement-II is true

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Two statements about degenerate orbitals and the hydrogen atom.

Find: Which option correctly identifies the truth value of Statement-I and Statement-II.

Statement-I: Orbitals having the same energy are called degenerate orbitals. This is the correct definition of degenerate orbitals, so Statement-I is true.

Statement-II: In the hydrogen atom, 3p3p and 3d3d orbitals are not degenerate orbitals. In a one-electron system like hydrogen, all orbitals with the same principal quantum number nn have the same energy. Therefore 3s3s, 3p3p and 3d3d are degenerate.

So Statement-II is false.

Therefore, the correct option is A: Statement-I is true but Statement-II is false.

Stepwise Analysis

Given: Statements involving the meaning of degenerate orbitals and the energy of orbitals in hydrogen.

Find: The most appropriate option.

  1. Analyze Statement-I: Orbitals with the same energy are called degenerate orbitals. This statement is true by definition.
  2. Analyze Statement-II: In the hydrogen atom, 3p3p and 3d3d are said to be not degenerate. This is false because in hydrogen all sublevels belonging to the same principal quantum level are degenerate.
  3. For n=3n = 3, the orbitals 3s3s, 3p3p and 3d3d have the same energy in hydrogen.
  4. Hence Statement-I is true and Statement-II is false.

The correct option is A.

Common mistakes

  • Assuming that orbitals with different shapes must always have different energies. This is wrong for the hydrogen atom, where energy depends only on the principal quantum number nn. Check whether the atom is a one-electron system before comparing orbital energies.

  • Confusing hydrogen with multi-electron atoms. In multi-electron atoms, ss, pp and dd orbitals of the same shell often differ in energy, but this rule does not apply to hydrogen. Use the special energy rule for one-electron species.

  • Reading Statement-II too quickly and missing the word not. That changes the truth value completely. Evaluate the full statement carefully before choosing the option.

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