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Chapter 7: Problem 62

Assume that a hydrogen atom's electron has been excited to the \(n=5\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

Short Answer

Expert verified
The hydrogen atom's electron at the \(n=5\) level can make \(4\) different transitions to lower energy levels (from \(n=5\) to \(n=4\), \(n=3\), \(n=2\), or \(n=1\)), each emitting a distinct wavelength of light. Therefore, \(4\) different wavelengths of light can be emitted.

Step by step solution

01

Identify the Possible Transitions

Since the electron is at the n=5 level, it can make transitions to any of the lower energy levels (n=4, n=3, n=2, or n=1).
02

Calculate the Number of Transitions

Each transition from the n=5 level to a lower energy level will correspond to a different wavelength of light. We can represent the transitions as follows: 1. From n=5 to n=4 2. From n=5 to n=3 3. From n=5 to n=2 4. From n=5 to n=1 Each of these transitions will emit a different wavelength of light. Thus, the number of different wavelengths emitted from the n=5 level is 4. In general, for an electron at energy level n, it can make (n-1) distinct transitions as it loses energy, resulting in (n-1) different wavelengths of light. Therefore, the answer is \(4\) different wavelengths of light.

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Most popular questions from this chapter

Predict the atomic number of the next alkali metal after francium and give its ground-state electron configuration.

Assume that we are in another universe with different physical laws. Electrons in this universe are described by four quantum numbers with meanings similar to those we use. We will call these quantum numbers \(p, q, r\), and \(s\). The rules for these quantum numbers are as follows: \(p=1,2,3,4,5, \ldots\) \(q\) takes on positive odd integers and \(q \leq p\). \(r\) takes on all even integer values from \(-q\) to \(+q\). (Zero is considered an even number.) \(s=+\frac{1}{2}\) or \(-\frac{1}{2}\) a. Sketch what the first four periods of the periodic table will look like in this universe. b. What are the atomic numbers of the first four elements you would expect to be least reactive? c. Give an example, using elements in the first four rows, of ionic compounds with the formulas XY, \(\mathrm{XY}_{2}, \mathrm{X}_{2} \mathrm{Y}, \mathrm{XY}_{3}\), and \(\mathrm{X}_{2} \mathrm{Y}_{3}\). d. How many electrons can have \(p=4, q=3 ?\) e. How many electrons can have \(p=3, q=0, r=0\) ? f. How many electrons can have \(p=6\) ?

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