Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

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

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

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

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

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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College Physics (Urone)

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Short Answer

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

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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