The potential energy of an electron in the fifth orbit of hydrogen atom is

Options

A. `0.54 eV`
B. `- 0.54 eV`
C. `1.08 eV`
D. `- 1.08 eV`

Explanation

To find the potential energy of an electron in the fifth orbit of a hydrogen atom, we can follow these steps:

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

### Step 2: Substitute the value of n
For the fifth orbit, \( n = 5 \). We can substitute this value into the formula:
\[ E = -\frac{13.6 \, \text{eV}}{5^2} = -\frac{13.6 \, \text{eV}}{25} \]

### Step 3: Calculate the total energy
Now we calculate the total energy:
\[ E = -\frac{13.6}{25} \, \text{eV} = -0.544 \, \text{eV} \]

### Step 4: Calculate the potential energy
The potential energy (U) of an electron in a hydrogen atom is related to the total energy by the formula:
\[ U = -2E \]
Substituting the value of \( E \):
\[ U = -2 \times (-0.544 \, \text{eV}) = 1.088 \, \text{eV} \]

### Step 5: Finalize the potential energy value
Since potential energy is typically expressed as a negative value in atomic physics, we write:
\[ U = -1.088 \, \text{eV} \]

Thus, the potential energy of an electron in the fifth orbit of a hydrogen atom is approximately:
\[ \boxed{-1.088 \, \text{eV}} \]