When the excited electron of a H atom from $$n = 5$$ drops to the ground state, the maximum number of emission lines observed are ______.

We need to find the maximum number of emission lines when an electron drops from $$n = 5$$ to the ground state ($$n = 1$$).

Use the formula for maximum emission lines

When an electron transitions from level $$n$$ to the ground state, the maximum number of spectral lines is given by:

$$\text{Number of lines} = \frac{n(n-1)}{2}$$

where $$n$$ is the initial energy level.

Substitute $$n = 5$$

$$\text{Number of lines} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} = 10$$

List all possible transitions

The 10 possible transitions are:

$$5 \rightarrow 4, \; 5 \rightarrow 3, \; 5 \rightarrow 2, \; 5 \rightarrow 1$$

$$4 \rightarrow 3, \; 4 \rightarrow 2, \; 4 \rightarrow 1$$

$$3 \rightarrow 2, \; 3 \rightarrow 1$$

$$2 \rightarrow 1$$

The answer is 10.