What is the trend of energy of Bohr's orbits?

Options

A. Energy of the orbit increases as we move away from the nucleus.
B. Energy of the orbit decreases as we move away from the nucleus.
C. Energy remains same as we move away from the nucleus.
D. Energy of Bohr's orbit cannot be calculated.

Explanation

To determine the trend of energy in Bohr's orbits, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Energy of Bohr's Orbits**:
The energy of an electron in a Bohr orbit is given by the formula:
\[ E_n = -\frac{13.6 \, Z^2}{n^2} \text{ eV} \]
where \( E_n \) is the energy of the orbit, \( Z \) is the atomic number, and \( n \) is the principal quantum number (the orbit number).

2. **Identify the Variables**:
- **Z**: Atomic number (for hydrogen, \( Z = 1 \)).
- **n**: Principal quantum number (1 for the first orbit, 2 for the second orbit, etc.).

3. **Calculate Energy for Different Orbits**:
- For the first orbit (\( n = 1 \)):
\[ E_1 = -\frac{13.6 \times 1^2}{1^2} = -13.6 \text{ eV} \]
- For the second orbit (\( n = 2 \)):
\[ E_2 = -\frac{13.6 \times 1^2}{2^2} = -\frac{13.6}{4} = -3.4 \text{ eV} \]

4. **Analyze the Results**:
- The energy for the first orbit is \(-13.6\) eV, and for the second orbit, it is \(-3.4\) eV.
- As \( n \) increases (moving to higher orbits), the energy value becomes less negative (increases).

5. **Conclusion**:
- The trend shows that as we move away from the nucleus (i.e., as \( n \) increases), the energy of the Bohr orbits increases. Therefore, the correct statement is:
- **Energy of the orbit increases as we move away from the nucleus.**

### Final Answer:
The trend of energy in Bohr's orbits is that the energy increases as we move away from the nucleus.

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