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Chapter 7: Problem 58

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
A hydrogen atom's electron excited to the \(n=5\) level can lose energy by transitioning to lower energy levels (\(n=1\), \(n=2\), \(n=3\), and \(n=4\)). There are 4 possible transitions, and each will emit a photon with a different wavelength. Therefore, there are 4 different wavelengths of light that can be emitted as the atom loses energy.

Step by step solution

01

Identify the initial and final energy levels

Initially, the electron is in the n=5 energy level, and it can lose energy by transitioning to lower energy levels (n=1, n=2, n=3, and n=4).
02

Calculate the possible transitions

To find the total number of possible transitions, we can consider each lower energy level: 1. Transition from n=5 to n=4 2. Transition from n=5 to n=3 3. Transition from n=5 to n=2 4. Transition from n=5 to n=1 Each of these transitions will emit a photon with a different wavelength, so there are 4 different wavelengths possible.
03

Check for any additional transitions

It is essential to check if there are any other transitions involving intermediate energy levels. In this case, there are no additional transitions since all lower energy levels have been considered directly from n=5.
04

Answer the question

As calculated in Step 2, there are 4 different wavelengths of light that can be emitted when a hydrogen atom's electron transitions from the n=5 energy level to the lower energy levels (n=1, n=2, n=3, and n=4).

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Most popular questions from this chapter

Valence electrons are those electrons in the outermost principal quantum level (highest \(n\) level) of an atom in its ground state. Groups \(1 \mathrm{~A}\) to \(8 \mathrm{~A}\) have from 1 to 8 valence electrons. For each group of the representative elements (1A-8A), give the number of valence electrons, the general valence electron configuration, a sample element in that group, and the specific valence electron configuration for that element.

Francium, Fr, is a radioactive element found in some uranium minerals and is formed as a result of the decay of actinium. a. What are the electron configurations of francium and its predicted most common ion? b. It has been estimated that at any one time, there is only one (1.0) ounce of francium on earth. Assuming this is true, what number of francium atoms exist on earth? c. The longest-lived isotope of francium is \({ }^{223} \mathrm{Fr}\). What is the total mass in grams of the neutrons in one atom of this isotope?

What are the possible values for the quantum numbers \(n, \ell\), and \(m_{\ell} ?\)

An excited hydrogen atom emits light with a wavelength of \(397.2 \mathrm{~nm}\) to reach the energy level for which \(n=2\). In which principal quantum level did the electron begin?

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set. a. \(n=3, \ell=2, m_{\ell}=2\) b. \(n=4, \ell=3, m_{\ell}=4\) c. \(n=0, \ell=0, m_{\ell}=0\) d. \(n=2, \ell=-1, m_{\ell}=1\)
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