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Chapter 34: Problem 3

Imagine an atom that, unlike hydrogen, had only three energy levels. If these levels were evenly spaced, how many spectral lines would result? How would their wavelengths compare?

Short Answer

Expert verified
The atom with three energy levels will produce 3 spectral lines. The wavelengths of these lines will be different from one another.

Step by step solution

01

Understand the relevant concepts

An energy level is a quantized level on which an electron resides within an atom. When an electron moves between these levels, it either emits or absorbs a specific amount of energy. This energy corresponds to specific wavelengths of light, which form the atomic spectrum. The number of spectral lines is determined by the number of distinct transitions an electron can make.
02

Calculate the number of spectral lines

Given that the atom in consideration has three energy levels, we use the formula for spectral lines calculations which is \( n(n-1)/2 \). Therefore, substituting \( n = 3 \) into the equation, we have: \( 3*(3-1)/2 = 3 \), hence there are 3 spectral lines in this atom.
03

Compare the Wavelengths

The wavelengths associated with each spectral line will be different because they correspond to the energy differences between different pairs of energy levels. Generally, transitions involving higher energy levels will result in emissions of light with shorter wavelengths, while transitions involving lower energy levels will result in emissions of light with longer wavelengths. Therefore, the spectral lines will have different wavelengths corresponding to the transitions between the different energy levels.

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