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An electron is confined in a harmonic potential well that has a spring constant of 10.5 N/m. What...

Question:

An electron is confined in a harmonic potential well that has a spring constant of 10.5 N/m. What is the longest wavelength of light that the electron can absorb? Express your answer with the appropriate units.

Spring Constant:

It is the necessary force to displace a particle of an elastic object from the mean position of the particle. This force varies with the material of the elastic object and the displacement from the mean position.

Answer and Explanation: 1


Given Data

  • The spring constant of the harmonic potential well is: {eq}k = 10.5\;{\rm{N}}/{\rm{m}} {/eq}.


The expression to calculate the longest wavelength of the light absorbed by the electron is:

{eq}\lambda = 2\pi c\sqrt {\dfrac{m}{k}} {/eq}

Here, {eq}c {/eq} is the speed of the light and its value is {eq}3 \times {10^8}\;{\rm{m}}/{\rm{s}} {/eq}, {eq}m {/eq} is the mass of the electron and its value is {eq}9.1 \times {10^{ - 31}}\;{\rm{kg}} {/eq}.

Substitute all the values in the above expression.

{eq}\begin{align*} \lambda &= 2\pi \left( {3 \times {{10}^8}\;{\rm{m}}/{\rm{s}}} \right)\sqrt {\dfrac{{9.1 \times {{10}^{ - 31}}\;{\rm{kg}}}}{{10.5\;{\rm{N}}/{\rm{m}}}}} \\ \lambda &= 5.5 \times {10^{ - 7}}\;{\rm{m}} \end{align*} {/eq}


Thus, the longest wavelength of the light absorbed by the electron is {eq}5.5 \times {10^{ - 7}}\;{\rm{m}} {/eq}.


Learn more about this topic:

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Practice Applying Spring Constant Formulas

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Chapter 17 / Lesson 11
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In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.


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