The energy of electron in first Bohr's orbit of `H-"atom"` is `- 13.6 eV` . What will be its potential energy in `n = 4^(th)` orbit.

Options

A. `- 14.6 eV`
B. `- 3.4 eV`
C. `- 0.85 eV`
D. `- 1.70 eV`

Explanation

To find the potential energy of an electron in the fourth orbit (n = 4) of a hydrogen atom, we can follow these steps:

### Step 1: Understand the Total Energy Formula
The total energy \( E_n \) of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)) and \( n \) is the principal quantum number (orbit number).

### Step 2: Substitute Values for n = 4
For the fourth orbit (n = 4):
\[ E_4 = -\frac{13.6 \, \text{eV} \cdot 1^2}{4^2} \]
\[ E_4 = -\frac{13.6 \, \text{eV}}{16} \]
\[ E_4 = -0.85 \, \text{eV} \]

### Step 3: Calculate the Potential Energy
The potential energy \( U \) in a hydrogen atom is related to the total energy \( E \) by the relation:
\[ U = 2E \]
Thus, for the fourth orbit:
\[ U_4 = 2 \times E_4 \]
\[ U_4 = 2 \times (-0.85 \, \text{eV}) \]
\[ U_4 = -1.70 \, \text{eV} \]

### Final Answer
The potential energy of the electron in the fourth orbit of a hydrogen atom is:
\[ \boxed{-1.70 \, \text{eV}} \]

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