Hydrogen atom:
The electronic ground state of hydrogen atom contains one electron in the first orbit. If sufficient energy is provided, this electron can be promoted to higher energy levels. The electronic energy of a hydrogen-like species (any atom//ions with nuclear charge Z and one electron) can be given as
`E_(n)=-(R_(H)Z^(2))/(n^(2))` where `R_(H)= "Rydberg constant," n= "principal quantum number"`
The energy required to promote the ground state electron of H-atom to the first excited state is:
When an electron returns from a higher energy level to a lower energy level, energy is given out in the form of UV//Visible radiation.

Answer

To solve the problem of calculating the energy required to promote the ground state electron of a hydrogen atom to the first excited state, we can follow these steps:

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

### Step 2: Identify the Energy Levels
For hydrogen:
- The ground state corresponds to \( n_1 = 1 \).
- The first excited state corresponds to \( n_2 = 2 \).

### Step 3: Calculate Energy for Ground State (n=1)
Using the formula for \( n_1 = 1 \):
\[ E_1 = -\frac{R_H \cdot 1^2}{1^2} = -R_H \]
Substituting \( R_H = 13.6 \, \text{eV} \):
\[ E_1 = -13.6 \, \text{eV} \]

### Step 4: Calculate Energy for First Excited State (n=2)
Using the formula for \( n_2 = 2 \):
\[ E_2 = -\frac{R_H \cdot 1^2}{2^2} = -\frac{R_H}{4} \]
Substituting \( R_H = 13.6 \, \text{eV} \):
\[ E_2 = -\frac{13.6}{4} = -3.4 \, \text{eV} \]

### Step 5: Calculate the Energy Difference
The energy required to promote the electron from the ground state to the first excited state is given by the difference in energy:
\[ \Delta E = E_2 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = (-3.4 \, \text{eV}) - (-13.6 \, \text{eV}) \]
\[ \Delta E = -3.4 + 13.6 = 10.2 \, \text{eV} \]

### Conclusion
The energy required to promote the ground state electron of the hydrogen atom to the first excited state is:
\[ \Delta E = 10.2 \, \text{eV} \]