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

When an electron transitions from a higher energy level to a lower one, it emits light at specific wavelengths, which correspond to spectral lines. In your case, we're looking at an electron jumping from the n=4 level to the ground state (n=1) in an atom. Let's break down how to determine the number of spectral lines emitted during this transition, especially when considering two atoms in the sample.

Understanding Electron Transitions

Electrons in an atom occupy discrete energy levels, denoted by quantum numbers (n=1, n=2, n=3, etc.). When an electron moves from a higher energy level to a lower one, it releases energy in the form of light. The energy difference between these levels corresponds to specific wavelengths of light, which we observe as spectral lines.

Calculating Spectral Lines

For an electron transitioning from n=4 to n=1, we need to consider all possible transitions it can make. The electron can move directly to the ground state or take intermediate steps. Here’s how we can visualize the possible transitions:

• Transition from n=4 to n=3
• Transition from n=3 to n=2
• Transition from n=2 to n=1
• Direct transition from n=4 to n=1

This results in the following 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

Counting the Lines

From the above transitions, we can see that there are a total of six possible transitions when considering the n=4 level down to the ground state. Each transition corresponds to a unique spectral line. Therefore, for one atom, there are six spectral lines emitted.

Considering Two Atoms

Now, if you have two atoms in your sample, each atom can independently emit the same spectral lines. However, the number of unique spectral lines emitted does not change because the transitions are the same for both atoms. Thus, while you will observe the same six spectral lines from each atom, the total number of emitted lines does not double; it remains six unique lines.

Summary

In summary, when an electron transitions from n=4 to the ground state (n=1), it can produce a total of six unique spectral lines. This count remains the same regardless of whether there is one atom or two atoms in the sample, as each atom will emit the same set of lines independently. Therefore, the answer to your question is that there are six spectral lines emitted when considering the electron's transition from n=4 to the ground state, regardless of the number of atoms present.