Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Question: What is the wavelength of EM radiation that ejects \(2.00\,{\rm{eV}}\) electrons from calcium metal, given that the binding energy is \(2.71\,{\rm{eV}}\)? What type of EM radiation is this?

Wavelength of the radiation is \(263 \times {10^{ - 9}}\,{\rm{m}}\)

Type of EM radiation is Ultra violet.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The longest-wavelength EM radiation can eject an electron

The kinetic energy of the electron is given by

\(K{E_e} = hf - BE\) ...(1)

Here \(K{E_e}\) is the kinetic energy, \(h\) is the plank constant, \(f\]) is the frequency of the EM radiation and \(BE\) is the binding energy.

Now we know that the wavelength of EM radiation is given by

\(\lambda = \frac{c}{f}\) ...(2)

Where \(c\) is the speed of light.

So equation becomes,

\(K{E_e} = \frac{{hc}}{\lambda } - BE\) ...(3)

Step 2: Wavelength of the radiation

The total energy of the photon is

\(\begin{array}{c}E = (2.00\,{\rm{eV}}) + (2.71\,{\rm{eV}})\\ = 4.71\,{\rm{eV}}\end{array}\)

We also know that: Planks constant \(h = 4.13 \times {10^{ - 15}}\,{\rm{eV}}{\rm{.s}}\)

Speed of light \(c = 3 \times {10^8}\,{\rm{m/s}}\)

The wavelength of the radiation is expressed as,

\(\lambda = \frac{{hc}}{E}\)

Substitute all the value in the above equation

\(\begin{array}{c}\lambda = \frac{{\left( {4.13 \times {{10}^{ - 15}}\,{\rm{eV}}{\rm{.s}}} \right)\left( {3 \times {{10}^8}\,{\rm{m/s}}} \right)}}{{(4.71\,{\rm{eV}})}}\\ = 263 \times {10^{ - 9}}\,{\rm{m}}\end{array}\)

Therefore, the wavelength of the radiation is \(263 \times {10^{ - 9}}\,{\rm{m}}\)

Hence, the wavelength of the EM radiation is \(263\,{\rm{nm,}}\) the radiation type is ultra violet.

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Short Answer

Question: What is the wavelength of EM radiation that ejects \(2.00\,{\rm{eV}}\) electrons from calcium metal, given that the binding energy is \(2.71\,{\rm{eV}}\)? What type of EM radiation is this?

Step by Step Solution

Step 1: The longest-wavelength EM radiation can eject an electron

Step 2: Wavelength of the radiation

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College Physics (Urone)

Answers without the blur.

Short Answer

Question: What is the wavelength of EM radiation that ejects \(2.00\,{\rm{eV}}\) electrons from calcium metal, given that the binding energy is \(2.71\,{\rm{eV}}\)? What type of EM radiation is this?

Step by Step Solution

Step 1: The longest-wavelength EM radiation can eject an electron

Step 2: Wavelength of the radiation

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