The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is

To determine the number of spectral lines emitted by an atomic hydrogen atom in the 4th energy level (n = 4) when it transitions to lower energy levels, we use the formula:

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

where n is the initial energy level.

Step 1: Substituting $n = 4$

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

 $$= \frac{4 \times 3}{2} = \frac{12}{2} = 6$$ 

Step 2: Understanding the Possible Transitions

An electron in the 4th energy level ($n = 4$) can transition to lower levels ($n = 3, 2, 1$), emitting photons with different wavelengths. The possible transitions are:

$4 \to 3$

$4 \to 2$

$4 \to 1$

$3 \to 2$

$3 \to 1$

$2 \to 1$

Each transition corresponds to a spectral line, confirming our calculation.

Final Answer:

Total possible transition = 6