The energies of orbitals of hydrogen atom are in the order

Options

A. `3s lt 3p lt 4s lt 3d lt 4p`
B. `3s lt 3p lt 3d lt 4s lt 4p`
C. `3s = 3p = 3d lt 4s = 4p `
D. `3s = 3p = 3d lt 4s lt 4p`

Answer

To determine the order of energies of the orbitals of a hydrogen atom, we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n) and Azimuthal Quantum Number (l)
For each orbital, we need to identify the principal quantum number (n) and the azimuthal quantum number (l). The values of l are as follows:
- For s orbitals, l = 0
- For p orbitals, l = 1
- For d orbitals, l = 2
- For f orbitals, l = 3

### Step 2: List the Orbitals and Their Quantum Numbers
The orbitals given are:
- 3s: n = 3, l = 0
- 3p: n = 3, l = 1
- 3d: n = 3, l = 2
- 4s: n = 4, l = 0
- 4p: n = 4, l = 1

### Step 3: Calculate n + l for Each Orbital
Now, we calculate the sum of n + l for each orbital:
- For 3s: n + l = 3 + 0 = 3
- For 3p: n + l = 3 + 1 = 4
- For 3d: n + l = 3 + 2 = 5
- For 4s: n + l = 4 + 0 = 4
- For 4p: n + l = 4 + 1 = 5

### Step 4: Compare n + l Values
Now we compare the n + l values:
- 3s: 3
- 3p: 4
- 3d: 5
- 4s: 4
- 4p: 5

### Step 5: Determine the Energy Order
According to the n + l rule:
- The lower the n + l value, the lower the energy.
- If two orbitals have the same n + l value, the one with the lower n value has lower energy.

From our calculations:
- The lowest energy is 3s (n + l = 3).
- Next, we have 3p and 4s (both n + l = 4). Since 3p has a lower n value than 4s, 3p has lower energy.
- Then we have 3d and 4p (both n + l = 5). Since 3d has a lower n value than 4p, 3d has lower energy.

### Final Energy Order
Thus, the order of energies from lowest to highest is:
1. 3s
2. 3p
3. 4s
4. 3d
5. 4p

### Answer
So the correct order of energies of the orbitals of the hydrogen atom is:
**3s < 3p < 4s < 3d < 4p**