The maximum number of photons emitted when an electron jumps from an energy level `n=4` to `n=1` is

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine the maximum number of photons emitted when an electron jumps from an energy level \( n=4 \) to \( n=1 \), we can follow these steps:

### Step 1: Understand the Energy Levels
In the Bohr model of the atom, electrons occupy discrete energy levels, denoted by quantum numbers \( n \). The electron can transition between these levels by absorbing or emitting energy in the form of photons.

### Step 2: Identify the Transition Levels
In this case, the electron is transitioning from \( n=4 \) to \( n=1 \). However, it can also pass through intermediate energy levels during this transition. The possible intermediate levels are \( n=3 \) and \( n=2 \).

### Step 3: Calculate the Possible Transitions
When an electron transitions from \( n=4 \) to \( n=1 \), it can do so in multiple steps:
1. From \( n=4 \) to \( n=3 \)
2. From \( n=3 \) to \( n=2 \)
3. From \( n=2 \) to \( n=1 \)

Each of these transitions corresponds to the emission of one photon. Therefore, the maximum number of photons emitted during this transition is 3.

### Step 4: General Formula for Maximum Transitions
For a general case where an electron transitions from a higher level \( n_2 \) to a lower level \( n_1 \), the maximum number of transitions (and thus photons emitted) can be calculated using the formula:
\[ \text{Maximum transitions} = n_2 - n_1 \]
In this case, \( n_2 = 4 \) and \( n_1 = 1 \), so:
\[ \text{Maximum transitions} = 4 - 1 = 3 \]

### Conclusion
Thus, the maximum number of photons emitted when an electron jumps from an energy level \( n=4 \) to \( n=1 \) is **3**.

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