Which of the following statements in relation to the...

Which of the following statements in relation to the hydrogen atom is incorrect? a. $3 \mathrm{~s}$ and $3 \mathrm{p}$ orbitals are of lower energy than $3 \mathrm{~d}$ orbital b. $3 \mathrm{p}$ orbital is lower in energy than $3 \mathrm{~d}$ orbital c. 3 s orbital is lower in energy than $3 \mathrm{p}$ orbital d. $3 \mathrm{~s}, 3 \mathrm{p}$ and $3 \mathrm{~d}$ orbitals all have the same energy

Which of the following statements in relation to the hydrogen atom is incorrect?
a. $3 \mathrm{~s}$ and $3 \mathrm{p}$ orbitals are of lower energy than $3 \mathrm{~d}$ orbital
b. $3 \mathrm{p}$ orbital is lower in energy than $3 \mathrm{~d}$ orbital
c. 3 s orbital is lower in energy than $3 \mathrm{p}$ orbital
d. $3 \mathrm{~s}, 3 \mathrm{p}$ and $3 \mathrm{~d}$ orbitals all have the same energy

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Key Concepts

Degeneracy in the Hydrogen Atom

In the hydrogen atom, the energy levels are determined solely by the principal quantum number (n). This unique characteristic means that all orbitals with the same n (for example, 3s, 3p, and 3d) have identical energy levels, regardless of their different angular momentum quantum numbers (l). This phenomenon, known as degeneracy, contrasts with multi-electron atoms where electron-electron interactions lead to energy differences among orbitals with the same principal quantum number.

Atomic Orbitals and Quantum Numbers

Atomic orbitals are regions around a nucleus where electrons are most likely to be found, and each is characterized by quantum numbers that define its properties. The principal quantum number (n) indicates the main energy level, while the angular momentum quantum number (l) defines the shape of the orbital (such as s, p, or d orbitals). In systems like the hydrogen atom, however, only n influences the energy, leading to the degeneracy of orbitals with different l values within the same principal energy level.

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