If n is the orbit number of the electron in a hydrogen atom, the correct statement among the following is

Options

A. electron energy increases as n increases.
B. hydrogen emits infrared rays for the electron tranition from `n=prop` to `n=1`.
C. electron energy is zero for `n=1`.
D. electron energy varies as `n^2`.

Explanation

To solve the question regarding the orbit number \( n \) of the electron in a hydrogen atom and to identify the correct statement, we will analyze each statement based on the principles of atomic physics.

### Step-by-Step Solution:

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

2. **Analyzing Statement 1:**
The first statement claims that "electron energy increases as \( n \) increases."
- From the formula, as \( n \) increases, \( n^2 \) increases, which makes \( E_n \) (the energy) more negative. However, since energy is negative, a less negative value means that the energy is increasing (becoming less bound).
- Thus, this statement is **correct**.

3. **Analyzing Statement 2:**
The second statement claims that "hydrogen emits infrared when the electron jumps from one orbit to another."
- The energy emitted during a transition can be calculated using the difference in energy levels. For transitions between the orbits, the emitted energy is not always in the infrared range. It depends on the specific orbits involved.
- Therefore, this statement is **incorrect**.

4. **Analyzing Statement 3:**
The third statement claims that "electron energy is 0 for \( n = 1 \)."
- Substituting \( n = 1 \) into the energy formula gives:
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]
- Hence, the energy is not 0, making this statement **incorrect**.

5. **Analyzing Statement 4:**
The fourth statement claims that "electron energy varies as \( n^2 \)."
- The energy varies as \( -\frac{1}{n^2} \), which means it is inversely proportional to \( n^2 \), not directly proportional. Therefore, this statement is also **incorrect**.

### Conclusion:
The only correct statement is that "electron energy increases as \( n \) increases."