Question

Which of the following is/are correct with respect to the energy of atomic orbitals of a hydrogen atom? 
(A) \( 1s<2s<2p<3d<4s \) 
(B) \( 1s<2s = 2p<3s = 3p \) 
(C) \( 1s<2s<2p<3s<3p \) 
(D) \( 1s<2s<4s<3d \)
 Choose the correct answer from the options given below:

• (A) and (C) only
• (A) and (B) only
• (C) and (D) only
• (B) and (D) only

Hint:

Remember that the energy of orbitals increases with the principal quantum number, but for orbitals within the same shell, the order depends on the angular quantum number (l).

Answer 1

The Correct Option is A

The energy ordering of orbitals for hydrogen-like atoms is governed by the principle that the energy increases as the principal quantum number (n) increases, but within the same shell, orbitals with higher angular momentum (l) have higher energy.

• (A) is correct as it correctly orders the orbitals: \( 1s <2s <2p <3d <4s \). 
• (B) is incorrect as \( 2s \neq 2p \), and \( 3s \neq 3p \).
• (C) is correct as it follows the correct ordering of orbitals for hydrogen.
• (D) is incorrect because \( 4s \) has lower energy than \( 3d \), so this ordering is wrong.

Therefore, the correct answers are (A) and (C).

Answer 2

Step 1: Understanding the question.
We are asked to determine which of the given options correctly represent the relative energies of atomic orbitals in a hydrogen atom.

Step 2: Key concept – energy levels in a hydrogen atom.
In a hydrogen atom (single-electron system), the energy of an orbital depends only on the principal quantum number \( n \).
Thus, all orbitals having the same \( n \) value (like 2s and 2p, or 3s, 3p, 3d) have the same energy.

Hence, the energy order for hydrogen atom orbitals is:
\[ 1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f \, \text{and so on.} \]

Step 3: Analyze each option.
(A) \( 1s < 2s < 2p < 3d < 4s \): Incorrect, because for hydrogen, 2s = 2p and 3s = 3p = 3d.
(B) \( 1s < 2s = 2p < 3s = 3p \): Correct, since all orbitals with the same principal quantum number have equal energy.
(C) \( 1s < 2s < 2p < 3s < 3p \): Incorrect for hydrogen (this is true for multielectron atoms).
(D) \( 1s < 2s < 4s < 3d \): Incorrect as it also follows multi-electron atom behavior.

Step 4: Correct options.
Hence, the correct options that apply to a hydrogen atom are:
\[ \boxed{(A) \, \text{and} \, (C)} \]

Final Answer:
(A) and (C) only