The binding energy of the electron in the lowest orbit of the hydrogen atom is 13.6 eV . The magnitudes energies from three lowest orbits of the hydrogen are

Options

A. 13.6, 6.8 , 8.4 eV
B. 13.6 , 10.2 , 3.4 eV
C. 13.6 , 27.2 , 40.8 eV
D. 13.6 ,3.4, 1.5 eV

Answer

To find the magnitudes of the energies from the three lowest orbits of the hydrogen atom, we will use the formula for the energy levels of the hydrogen atom:

### Step-by-Step Solution:

1. **Understanding the Formula**:
The energy of an electron in a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( E_n \) is the energy at the nth orbit and \( n \) is the principal quantum number (orbit number).

2. **Calculating Energy for the First Orbit (n=1)**:
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]
The magnitude of this energy is \( 13.6 \, \text{eV} \).

3. **Calculating Energy for the Second Orbit (n=2)**:
\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} = -3.4 \, \text{eV} \]
The magnitude of this energy is \( 3.4 \, \text{eV} \).

4. **Calculating Energy for the Third Orbit (n=3)**:
\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} \approx -1.51 \, \text{eV} \]
The magnitude of this energy is approximately \( 1.5 \, \text{eV} \).

5. **Summarizing the Results**:
The magnitudes of the energies from the three lowest orbits are:
- For n=1: \( 13.6 \, \text{eV} \)
- For n=2: \( 3.4 \, \text{eV} \)
- For n=3: \( 1.5 \, \text{eV} \)

### Final Answer:
The magnitudes of the energies from the three lowest orbits of the hydrogen atom are \( 13.6 \, \text{eV}, 3.4 \, \text{eV}, \) and \( 1.5 \, \text{eV} \).