The transition of electron in if atom that will emit maximum energy is

Options

A. `n_(3) rarr n_(2)`
B. `n_(4) rarr n_(3)`
C. `n_(2) rarr n_(4)`
D. `n_(6) rarr n_(5)`

Explanation

To determine the transition of an electron in an atom that will emit maximum energy, we can follow these steps:

### Step 1: Understand the Energy Formula
The energy of an electron in an atom is given by the formula:
\[ E = -\frac{13.6 Z^2}{n^2} \]
where \( E \) is the energy, \( Z \) is the atomic number, and \( n \) is the principal quantum number.

### Step 2: Analyze the Relationship Between Energy and n
From the formula, we can see that energy \( E \) is inversely proportional to the square of the principal quantum number \( n \):
\[ E \propto \frac{1}{n^2} \]
This means that as \( n \) increases, the energy \( E \) decreases.

### Step 3: Determine the Condition for Maximum Energy
To achieve maximum energy, we need to minimize the value of \( n \). The lowest value of \( n \) in a hydrogen-like atom is \( n = 1 \).

### Step 4: Identify the Possible Transitions
Given the options for transitions (for example, from \( n_2 \) to \( n_1 \), \( n_3 \) to \( n_2 \), etc.), we need to find the transition that involves the smallest \( n \) value.

### Step 5: Evaluate the Transitions
- Transition from \( n_2 \) to \( n_1 \) (maximum energy emission)
- Transition from \( n_3 \) to \( n_2 \) (less energy)
- Transition from \( n_4 \) to \( n_3 \) (even less energy)
- Transition from \( n_6 \) to \( n_5 \) (least energy)

Among these transitions, the transition from \( n_2 \) to \( n_1 \) will emit the maximum energy because it involves the largest change in energy levels.

### Conclusion
The transition of an electron in an atom that will emit maximum energy is the transition from \( n_2 \) to \( n_1 \).

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