If electron in a hydrogen atom has moves from n = 1 to n = 10 orbit, the potential energy of the system has

Options

A. increased
B. decreased
C. remained unchanged
D. become zero

Answer

To solve the problem of how the potential energy of an electron in a hydrogen atom changes when it moves from the n = 1 orbit to the n = 10 orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Potential Energy**:
The potential energy (U) of an electron in a hydrogen atom is given by the formula:
\[ U = -\frac{Z e^2}{4 \pi \epsilon_0 r} \]
where \(Z\) is the atomic number (for hydrogen, \(Z = 1\)), \(e\) is the charge of the electron, \(\epsilon_0\) is the permittivity of free space, and \(r\) is the radius of the orbit.

2. **Relate the Radius to the Principal Quantum Number (n)**:
The radius of the nth orbit in a hydrogen atom is proportional to \(n^2\):
\[ r_n \propto n^2 \]
Therefore, we can express the potential energy in terms of \(n\):
\[ U_n = -\frac{e^2}{4 \pi \epsilon_0} \cdot \frac{1}{r_n} \propto -\frac{1}{n^2} \]

3. **Calculate the Potential Energy for n = 1 and n = 10**:
- For \(n = 1\):
\[ U_1 \propto -\frac{1}{1^2} = -1 \]
- For \(n = 10\):
\[ U_{10} \propto -\frac{1}{10^2} = -\frac{1}{100} \]

4. **Compare the Potential Energies**:
As \(n\) increases, the potential energy becomes less negative (i.e., it increases in value):
- \(U_1 = -1\)
- \(U_{10} = -0.01\)

5. **Conclusion**:
Since the potential energy is increasing in value (becoming less negative) as the electron moves from \(n = 1\) to \(n = 10\), we can conclude that the potential energy of the system has increased.

### Final Answer:
The potential energy of the system has increased as the electron moves from n = 1 to n = 10.

---