The number of spectral lines in hydrogen atom are

Options

A. `R[(1)/(4^(2)) - (1)/(5^(2))]`
B. `R[(1)/(3^(2)) - (1)/(4^(2))]`
C. `R[(1)/(2^(2)) - (1)/(3^(2))]`
D. `R[(1)/(5^(2)) - (1)/(6^(2))]`

Answer

To determine the number of spectral lines in a hydrogen atom, we can follow these steps:

### Step 1: Understand Spectral Lines
Spectral lines are produced when electrons transition between different energy levels in an atom. When an electron jumps from a higher energy level to a lower one, it emits energy in the form of light, which corresponds to a spectral line.

### Step 2: Identify Energy Levels
In a hydrogen atom, the energy levels are quantized and can be represented as n = 1, 2, 3, ..., ∞ (where n is the principal quantum number). The transitions occur between these levels.

### Step 3: Calculate the Number of Transitions
The number of spectral lines (N) produced when an electron transitions from a higher energy level (n_i) to a lower energy level (n_f) can be calculated using the formula:
\[ N = \frac{n(n-1)}{2} \]
where n is the number of energy levels involved in the transitions.

### Step 4: Consider Infinite Energy Levels
For hydrogen, if we consider transitions from an infinite energy level (n = ∞) to any lower level (n = 1, 2, 3, ...), the number of possible transitions becomes infinite. This is because an electron can transition from ∞ to any of the lower levels, resulting in an infinite number of spectral lines.

### Conclusion
Thus, the number of spectral lines in a hydrogen atom is infinite.

### Final Answer
The number of spectral lines in a hydrogen atom is infinite.

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