If `R_(H)` represents Rydberg constant, then the energy of the electron in the ground state of hydrogen atom is

Options

A. `- (hc)/(R_(H))`
B. `- (1)/(R_(H) ch)`
C. `-R_(H) ch`
D. `- (R_(H)c)/(h)`

Explanation

To find the energy of the electron in the ground state of a hydrogen atom, we can use the formula derived from the Bohr model of the atom. Here’s a step-by-step solution:

### Step 1: Understand the Formula
The energy of an electron in a hydrogen atom can be expressed using the formula:
\[ E_n = -\frac{R_H \cdot Z^2}{n^2} \]
where:
- \(E_n\) is the energy of the electron in the nth energy level,
- \(R_H\) is the Rydberg constant (approximately \(13.6 \, \text{eV}\)),
- \(Z\) is the atomic number (for hydrogen, \(Z = 1\)),
- \(n\) is the principal quantum number (for ground state, \(n = 1\)).

### Step 2: Substitute Values
For hydrogen:
- \(Z = 1\)
- \(n = 1\)

Substituting these values into the formula gives:
\[ E_1 = -\frac{R_H \cdot 1^2}{1^2} = -R_H \]

### Step 3: Final Expression
Thus, the energy of the electron in the ground state of a hydrogen atom is:
\[ E_1 = -R_H \]
Since \(R_H\) is approximately \(13.6 \, \text{eV}\), we can express this as:
\[ E_1 = -13.6 \, \text{eV} \]

### Conclusion
The energy of the electron in the ground state of a hydrogen atom is:
\[ E_1 = -13.6 \, \text{eV} \]