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Chapter 2: Problem 129

Cesium was discovered in natural mineral waters in 1860 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.

Short Answer

Expert verified
The frequency of the photon is approximately \(6.585 \times 10^{14} \, Hz\) and the energy of the photon is approximately \(4.359 \times 10^{-19} \, J\).

Step by step solution

01

Convert wavelength to meters

First, we need to convert the given wavelength (455.5 nm) to meters. We know that 1 nm is equal to \(1 \times 10^{-9}\) m. So, we can convert the wavelength to meters as follows: \(455.5 \, nm \times \frac{1\,m}{1 \times 10^9\, nm} = 4.555 \times 10^{-7} \, m\)
02

Calculate the frequency

Next, we will use the equation \(ν = \frac{c}{λ}\) to calculate the frequency of the photon. The speed of light (c) is approximately \(3 \times 10^8 \, m/s\). So, the frequency will be: \(ν = \frac{3 \times 10^8\, m/s}{4.555 \times 10^{-7}\, m} ≈ 6.585 \times 10^{14} \, Hz\)
03

Calculate the energy

Finally, we will calculate the energy of the photon using Planck's constant (h) and the frequency (ν). Planck's constant is approximately \(6.626 \times 10^{-34} \, Js\). The energy of the photon can be calculated as follows: \(E = hν = (6.626 \times 10^{-34}\, Js)(6.585 \times 10^{14}\, Hz) ≈ 4.359 \times 10^{-19} \, J\) So, the frequency of the photon is approximately \(6.585 \times 10^{14} \, Hz\) and the energy of the photon is approximately \(4.359 \times 10^{-19} \, J\).

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Most popular questions from this chapter

One of the visible lines in the hydrogen emission spectrum corresponds to the \(n=6\) to \(n=2\) electronic transition. What color light is this transition? See Exercise \(138 .\)

Calculate the velocities of electrons with de Broglie wavelengths of \(1.0 \times 10^{2} \mathrm{nm}\) and \(1.0 \mathrm{nm} .\)

Give a possible set of values of the four quantum numbers for the \(4 s\) and \(3 d\) electrons in titanium.

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. \(n=4 \rightarrow n=3\) b. \(n=5 \rightarrow n=4\) c. \(n=5 \rightarrow n=3\)

Determine the maximum number of electrons that can have each of the following designations: \(2 f, 2 d_{x y}, 3 p, 5 d_{y z},\) and \(4 p\).
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