The orbital nearest to the nucleus is

Options

A. 4f
B. 5d
C. 4s
D. 7p

Answer

To determine which orbital is nearest to the nucleus, we need to analyze the principal quantum number and the energy levels of the orbitals mentioned in the question. Here’s a step-by-step solution:

### Step 1: Understand Principal Quantum Number
The principal quantum number (n) indicates the main energy level of an electron in an atom. The lower the value of n, the closer the orbital is to the nucleus.

**Hint:** Remember that n = 1 is closer to the nucleus than n = 2, and so on.

### Step 2: Identify the Orbitals
The question mentions two orbitals: 4f and 4s. Both of these orbitals have the same principal quantum number (n = 4).

**Hint:** When comparing orbitals, always check their principal quantum numbers first.

### Step 3: Apply the n + l Rule
Since both orbitals have the same principal quantum number, we need to compare their energy using the n + l rule. The n + l rule states that the orbital with the lower value of n + l will have lower energy and will be closer to the nucleus.

- For 4f:
- n = 4
- l (for f orbital) = 3
- n + l = 4 + 3 = 7

- For 4s:
- n = 4
- l (for s orbital) = 0
- n + l = 4 + 0 = 4

**Hint:** Calculate n + l for each orbital to compare their energies.

### Step 4: Compare Energies
Now we compare the n + l values:
- 4f has n + l = 7
- 4s has n + l = 4

Since 4s has a lower n + l value than 4f, it has lower energy and is therefore closer to the nucleus.

**Hint:** The lower the n + l value, the closer the orbital is to the nucleus.

### Step 5: Conclusion
The orbital nearest to the nucleus is 4s.

**Final Answer:** The orbital nearest to the nucleus is **4s**.