The only element in the hydrogen atom resides under ordinary condition on the first orbit .When energy is supplied the element move to hjgher energy ornbit depending on the lower of energy absioerbed .When this electron to may of the electron return to any of the lower orbits, it emit energy Lyman series is formed when the electron to the lowest orbit white Balmer series ids formed when the electron returns to the second orbit similar Paschen Brackett, and Pfund series are formed when electron return to the third fourth , and fifth arbit from highest energy orbits, respectively
Maximum number of liner produced is equal when as electron jumps from nth level to ground level is equal to `(n(n - 1))/(2)`If teh electron comes back from the energy level having energy `E_(2)` to the energy level having energy `E_(1)` then the difference may be expresent in terms of energy of photon as `E_(2) - E_(1) = Delta E, lambda = hc//Delta E` Since h and c are constants `Delta E` coresponding to definite energy , thus , each transition from one energy level to unother will produce a light of definite wavelem=ngth .This isd actually observed as a line in the spectrum of hydrogen atom Wave number of line is given by the formula `bar v = RZ^(2)((1)/(n_(1)^(2))- (1)/(n_(12)^(2)))`Where R is a Rydherg constant
Its a single isolated atom, an electrons make transition from fifth excited state is second thern maximum number of different type of photon observed is

Options

A. 3
B. 4
C. 6
D. 15

Explanation

To solve the problem, we need to determine the maximum number of different types of photons emitted when an electron transitions from the fifth excited state to the second excited state in a hydrogen atom.

### Step-by-Step Solution:

1. **Identify the Energy Levels**:
- The fifth excited state corresponds to \( n = 6 \) (since the ground state is \( n = 1 \)).
- The second excited state corresponds to \( n = 3 \).

2. **Determine the Transition Path**:
- The electron will transition from \( n = 6 \) to \( n = 3 \).
- During this transition, the electron can pass through the intermediate energy levels, which are \( n = 5 \), \( n = 4 \), and \( n = 3 \).

3. **Count the Transitions**:
- The possible transitions are:
- From \( n = 6 \) to \( n = 5 \)
- From \( n = 5 \) to \( n = 4 \)
- From \( n = 4 \) to \( n = 3 \)
- Each transition corresponds to the emission of a photon.

4. **Calculate the Number of Different Photons**:
- Each transition can emit a different photon. Therefore, the total number of different types of photons emitted during these transitions is equal to the number of transitions:
- Transition 1: \( n = 6 \) to \( n = 5 \) (1 photon)
- Transition 2: \( n = 5 \) to \( n = 4 \) (1 photon)
- Transition 3: \( n = 4 \) to \( n = 3 \) (1 photon)
- Thus, the total number of different types of photons emitted is \( 3 \).

### Final Answer:
The maximum number of different types of photons observed when the electron transitions from the fifth excited state to the second excited state is **3**.

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