Which of the following statements is not correct?

Options

A. the shape of an atomic orbital depends on the azimuthal quantum number.
B. the orientation of an atomic orbital depends on the magnetic quantum number.
C. The energy of an electron in an atomic orbital of multi-electron atom depends on principal quantum number.
D. The number of degenerate atomic orbitals of one type depends on the values of azimuthal and magnetic quantum numbers.

Answer

To determine which statement is not correct, we will analyze each option provided in the question.

### Step 1: Analyze Option A
**Statement A:** The shape of atomic orbitals depends on the azimuthal quantum number (L).

- The azimuthal quantum number (L) indeed determines the shape of the atomic orbitals.
- For example:
- L = 0 corresponds to s-orbitals (spherical shape).
- L = 1 corresponds to p-orbitals (dumbbell shape).
- L = 2 corresponds to d-orbitals (double dumbbell shape).
- **Conclusion:** This statement is correct.

**Hint:** Remember that the azimuthal quantum number defines the shape of the orbital.

### Step 2: Analyze Option B
**Statement B:** The orientation of an atomic orbital depends on the magnetic quantum number (m).

- The magnetic quantum number (m) specifies the orientation of the orbital in space.
- For example, in the p-orbitals (L = 1), there are three orientations: px, py, and pz, corresponding to m values of -1, 0, and +1.
- **Conclusion:** This statement is correct.

**Hint:** The magnetic quantum number gives the specific orientation of the orbitals.

### Step 3: Analyze Option C
**Statement C:** The energy of an electron in an atomic orbital of a multi-electron atom depends on the principal quantum number (n).

- While the principal quantum number (n) does influence the energy levels, in multi-electron atoms, the energy of an electron also depends on the azimuthal quantum number (L) due to electron-electron interactions and shielding effects.
- Therefore, saying it depends only on n is incorrect.
- **Conclusion:** This statement is not correct.

**Hint:** Consider how electron interactions in multi-electron atoms affect energy levels.

### Step 4: Analyze Option D
**Statement D:** The number of degenerate orbitals of one type depends on the value of the azimuthal and magnetic quantum number.

- Degenerate orbitals are orbitals that have the same energy level. The number of degenerate orbitals for a given value of L is determined by the magnetic quantum number (m).
- For example, for L = 1 (p orbitals), there are three degenerate orbitals (px, py, pz).
- **Conclusion:** This statement is correct.

**Hint:** Degenerate orbitals are determined by the values of L and m.

### Final Conclusion
After analyzing all options, the statement that is not correct is **Option C**: "The energy of an electron in an atomic orbital of a multi-electron atom depends on the principal quantum number."

Thus, the answer is **C**.