Total energy of electron in nth stationary orbit of hydrogen atom is

Options

A. `(-13.6)/(n)eV`
B. `(-13.6)/(n^2)eV`
C. `(-136)/(n)eV`
D. `(-136)/(n^2)eV`

Explanation

To find the total energy of an electron in the nth stationary 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:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]

### Step 2: Identify the value of Z
For a hydrogen atom, the atomic number \( Z \) is 1. Therefore, we can substitute \( Z \) into the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot 1^2}{n^2} \]

### Step 3: Simplify the equation
This simplifies to:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

### Step 4: Interpret the result
This equation shows that the total energy of the electron in the nth orbit is negative, indicating that the electron is bound to the nucleus. The energy becomes less negative (increases) as \( n \) increases, meaning the electron is less tightly bound at higher energy levels.

### Final Result
Thus, the total energy of the electron in the nth stationary orbit of a hydrogen atom is:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

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