The total energy of an electron in 4th orbit of hydrogen atom is

Options

A. `-13.6eV`
B. `-3.4eV`
C. `-1.51eV`
D. `-0.85eV`

Explanation

To find the total energy of an electron in the 4th orbit of a hydrogen atom, we can use the formula for the energy of an electron in a hydrogen-like atom:

\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

where:
- \( E_n \) is the energy of the electron in the nth orbit,
- \( n \) is the principal quantum number (orbit number),
- 13.6 eV is the ionization energy of hydrogen.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number:**
For the 4th orbit, the principal quantum number \( n = 4 \).

2. **Substitute the Value of n into the Energy Formula:**
We substitute \( n = 4 \) into the energy formula:
\[ E_4 = -\frac{13.6 \, \text{eV}}{4^2} \]

3. **Calculate \( 4^2 \):**
Calculate \( 4^2 \):
\[ 4^2 = 16 \]

4. **Substitute \( 16 \) into the Energy Formula:**
Now substitute \( 16 \) back into the equation:
\[ E_4 = -\frac{13.6 \, \text{eV}}{16} \]

5. **Perform the Division:**
Now, perform the division:
\[ E_4 = -0.85 \, \text{eV} \]

### Final Answer:
The total energy of the electron in the 4th orbit of a hydrogen atom is:
\[ E_4 = -0.85 \, \text{eV} \]