what are the number of spectral lines when electron jumps from n=4 to ground state if two atoms are present in the sample

When considering the number of spectral lines produced by electron transitions in atoms, it's essential to understand how these transitions occur and how they relate to the energy levels of the electrons. In your scenario, where electrons jump from the n=4 energy level to the ground state (n=1) in two atoms, we can break down the process step by step.

Energy Levels and Transitions

In an atom, electrons occupy specific energy levels, denoted by quantum numbers (n=1, 2, 3, 4, etc.). When an electron transitions from a higher energy level to a lower one, it emits energy in the form of light, which corresponds to a spectral line. The number of spectral lines produced depends on the possible transitions between these energy levels.

Calculating Possible Transitions

For an electron transitioning from n=4 to n=1, we can identify the possible transitions:

• n=4 to n=3
• n=4 to n=2
• n=4 to n=1
• n=3 to n=2
• n=3 to n=1
• n=2 to n=1

Each of these transitions results in the emission of a photon, creating a distinct spectral line. To find the total number of unique transitions, we can use the formula for combinations:

Combination Formula

The number of ways to choose two levels from n levels is given by the formula:

C(n, 2) = n(n-1)/2

In this case, we have energy levels n=1, 2, 3, and 4, which gives us 4 levels. The number of unique transitions (or spectral lines) can be calculated as follows:

C(4, 2) = 4(4-1)/2 = 6

Considering Two Atoms

Now, since you have two atoms in the sample, each atom can independently undergo these transitions. Therefore, the total number of spectral lines produced by both atoms would be:

Total Spectral Lines = Number of Lines from One Atom × Number of Atoms

Thus, if one atom produces 6 spectral lines, two atoms would produce:

Total = 6 × 2 = 12

Summary

In summary, when electrons transition from n=4 to the ground state in two atoms, a total of 12 spectral lines will be observed. Each transition corresponds to a unique energy difference, resulting in distinct wavelengths of emitted light, which can be detected as spectral lines in a spectrum.