According to Bohr Model for Hydrogen, energy is proportional to :

Options

A. `-Z^(2)//n`
B. `-n//Z^(2)`
C. `-Z^(2)//n^(2)`
D. `-n^(2)//Z`

Answer

To solve the question regarding the proportionality of energy according to Bohr's model for hydrogen, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bohr's Model**:
- Bohr's model describes the behavior of electrons in hydrogen-like atoms. It quantifies the energy levels of electrons in orbits around the nucleus.

2. **Energy Formula**:
- According to Bohr's model, the energy of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, Z^2}{n^2} \, \text{eV} \]
- Here, \(E_n\) is the energy of the nth orbit, \(Z\) is the atomic number (which is 1 for hydrogen), and \(n\) is the principal quantum number (n = 1, 2, 3,...).

3. **Identifying Proportionality**:
- From the formula, we can see that the energy \(E_n\) is proportional to \(-\frac{Z^2}{n^2}\).
- This means that as \(n\) increases, the energy becomes less negative (or increases), and it is also dependent on the square of the atomic number \(Z\).

4. **Conclusion**:
- Therefore, according to Bohr's model for hydrogen, the energy is proportional to:
\[ -\frac{Z^2}{n^2} \]
- Since \(Z = 1\) for hydrogen, this simplifies to \(-\frac{1}{n^2}\).

### Final Answer:
The energy according to Bohr's model for hydrogen is proportional to \(-\frac{Z^2}{n^2}\).