answer parts a and b magnesium metal foil was illuminated by a pulse of laser beam with a wavelength of 306 nm. Atotal number of 6 × 10³ ejected electrons were generated. Each electron has an de Brogliewavelength of 2 nm.(a) Calculate the work function (express the answer in eV)(b) Calculate the threshold frequency (express the answer in nm).

The de Broglie wavelength () of a particle with momentum is given by:where is Planck's constant (…

Answered: magnesium metal foil was illuminated by…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

answer parts a and b

magnesium metal foil was illuminated by a pulse of laser beam with a wavelength of 306 nm. A
total number of 6 × 10³ ejected electrons were generated. Each electron has an de Broglie
wavelength of 2 nm.
(a) Calculate the work function (express the answer in eV)
(b) Calculate the threshold frequency (express the answer in nm).

Expert Solution

Step 1: de Broglie relation and Photoelectric effect formula

The de Broglie wavelength ( $lambda$ ) of a particle with momentum $p$ is given by:

$lambda equals h over p$

where $h$ is Planck's constant ( $6.626 cross times 10 to the power of negative 34 end exponent$ J·s) and $p$ is the momentum of the particle.

The photoelectric effect relates the energy of a photon to the work function ( $straight capital phi$ ) and the kinetic energy of the emitted electron ( $K. E.$ ):

$E subscript text photon end text end subscript equals straight capital phi plus K. E.$

Given that $E subscript text photon end text end subscript equals h nu$ , where $h$ is Planck's constant and $nu$ is the frequency of the incident light.

The kinetic energy ( $K. E.$ ) of the emitted electron can be expressed in terms of its velocity ( $v$ ) as:

$K. E. equals 1 half m v squared$

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