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Chapter 7: Problem 155

Assume that a hydrogen atom's electron has been excited to the \(n=6\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

Short Answer

Expert verified
When a hydrogen atom's electron is excited to the \(n=6\) level, it can transition to any of the lower energy levels (n=1, 2, 3, 4, 5). There are 5 possible transitions to lower energy levels, meaning that there will be 5 different wavelengths of light that can be emitted as the excited hydrogen atom loses energy.

Step by step solution

01

List all the possible energy levels the electron can transition to from n=6

For a hydrogen atom, the possible energy levels for the electron are given by integer values n=1, 2, 3, ..., ∞, where n=1 is the ground state (lowest energy level) and the energy level increases as n increases. Since the electron is excited to n=6, it can potentially transition to any of the lower energy levels (n=1, 2, 3, 4, 5).
02

Determine the number of possible transitions

Now, we will count all the possible transitions the electron can make from n=6 to lower energy levels. We can represent these transitions as follows: 1. Transition from n=6 to n=5 2. Transition from n=6 to n=4 3. Transition from n=6 to n=3 4. Transition from n=6 to n=2 5. Transition from n=6 to n=1
03

Count the number of possible transitions

We have listed five possible transitions the electron can make from the n=6 energy level. These transitions correspond to the electron releasing energy in the form of light, resulting in different wavelengths of emitted light. Therefore, there are 5 different wavelengths of light that can be emitted as the excited hydrogen atom loses energy.

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Most popular questions from this chapter

Cesium was discovered in natural mineral waters in \(1860 \mathrm{by}\) R. W. Bunsen and G. R. Kirchhoff using the spectroscope they invented in \(1859 .\) The name came from the Latin caesius ("sky blue") because of the prominent blue line observed for this element at \(455.5 \mathrm{~nm} .\) Calculate the frequency and energy of a photon of this light.

Arrange the following groups of atoms in order of increasing size. a. \(\mathrm{Te}, \mathrm{S}, \mathrm{Se}\) b. \(\mathrm{K}, \mathrm{Br}, \mathrm{Ni}\) c. \(\mathrm{Ba}, \mathrm{Si}, \mathrm{F}\)

Identify the following elements. a. An excited state of this element has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\). b. The ground-state electron configuration is [Ne] \(3 s^{2} 3 p^{4}\). c. An excited state of this element has the electron configuration \([\mathrm{Kr}] 5 s^{2} 4 d^{6} 5 p^{2} 6 s^{1}\) d. The ground-state electron configuration contains three unpaired \(6 p\) electrons.

The wave function for the \(2 p_{z}\) orbital in the hydrogen atom is $$ \psi_{2 p_{i}}=\frac{1}{4 \sqrt{2 \pi}}\left(\frac{Z}{a_{0}}\right)^{3 / 2} \sigma \mathrm{e}^{-\sigma / 2} \cos \theta $$ where \(a_{0}\) is the value for the radius of the first Bohr orbit in meters \(\left(5.29 \times 10^{-11}\right), \sigma\) is \(Z\left(r / a_{0}\right), r\) is the value for the distance from the nucleus in meters, and \(\theta\) is an angle. Calculate the value of \(\psi_{2 p_{z}}^{2}\) at \(r=a_{0}\) for \(\theta=0^{\circ}(z\) axis \()\) and for \(\theta=90^{\circ}\) \((x y\) plane).

Consider the following approximate visible light spectrum: Barium emits light in the visible region of the spectrum. If each photon of light emitted from barium has an energy of \(3.59 \times 10^{-19} \mathrm{~J}\), what color of visible light is emitted?
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