The magnitude of energy, the magnitude of linear momentum and orbital radius of an electron in a hydrogen atom corresponding to the quantum number n are `E, P` and r respectively. Then according to Bohr's theory of hydrogen atom:

Options

A. Epr is proportinal to `(1)/(n)`
B. P/E is proportional to n
C. Er is constant for all orbits
D. Pr is proportional to n

Answer

To solve the problem, we need to analyze the relationships between the energy (E), linear momentum (P), and orbital radius (r) of an electron in a hydrogen atom according to Bohr's theory.

### Step-by-Step Solution:

1. **Energy of the Electron (E)**:
According to Bohr's theory, the energy of an electron in a hydrogen atom is given by:
\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]
This shows that the energy is inversely proportional to the square of the principal quantum number \(n\):
\[ E \propto \frac{1}{n^2} \]

2. **Linear Momentum of the Electron (P)**:
The linear momentum of the electron can be expressed as:
\[ P_n = m v_n \]
where \(v_n\) is the velocity of the electron in the nth orbit. From Bohr's model, we find that:
\[ v_n \propto \frac{1}{n} \]
Therefore, the momentum is also inversely proportional to \(n\):
\[ P \propto \frac{1}{n} \]

3. **Orbital Radius of the Electron (r)**:
The radius of the electron's orbit is given by:
\[ r_n = n^2 a_0 \]
where \(a_0\) is the Bohr radius. This shows that the radius is directly proportional to the square of the quantum number \(n\):
\[ r \propto n^2 \]

4. **Analyzing Relationships**:
Now we can summarize the relationships:
- \(E \propto \frac{1}{n^2}\)
- \(P \propto \frac{1}{n}\)
- \(r \propto n^2\)

5. **Finding the Relationships**:
We can analyze the ratios:
- For \(E \cdot P \cdot r\):
\[ E \cdot P \cdot r \propto \left(\frac{1}{n^2}\right) \cdot \left(\frac{1}{n}\right) \cdot (n^2) = \frac{1}{n^2} \cdot \frac{1}{n} \cdot n^2 = \frac{1}{n} \]
- For \(\frac{E}{P}\):
\[ \frac{E}{P} \propto \frac{\frac{1}{n^2}}{\frac{1}{n}} = \frac{1}{n} \]
- For \(E \cdot r\):
\[ E \cdot r \propto \left(\frac{1}{n^2}\right) \cdot (n^2) = 1 \]

6. **Conclusion**:
From the analysis, we find that:
- \(E \cdot r\) is constant.
- \(\frac{E}{P}\) is not constant.
- \(E \cdot P \cdot r\) is not constant.

Thus, the correct relationship according to Bohr's theory is that \(E \cdot r\) is constant for all orbits.

### Final Answer:
The correct option is \(C\): \(E \cdot r\) is constant.