9. Quantum Mechanics

Photoelectric Effect

Addressing a common misconception about the photoelectric effect

An X-ray photon of wavelength 0.989 nm strikes a surface. The 
emitted electron has a kinetic energy of 969 eV. What is the 
binding energy of the electron in kJ>mol? 
[KE = 12 
mv2; 1 electron volt (eV) = 1.602 * 10 - 19 J]

 A metal emits electrons when light of a certain frequency shines on it. 

 Correct, there is a threshold energy needed. 

 Classical mechanics failed to predict the radiation given off by blackbodies. 

 This statement is true but describes the phenomenon of blackbody radiation. 

 An electron is emitted by a metal after enough photons have been absorbed. 

 There is a threshold energy requirement for the photons. 

 Waves cancel each other out or build each other up. 

 This describes destructive and constructive interference. 

 None of the above accurately describes the photoelectric effect. 

 One of the choice does characterize the photoelectric effect. 

 The photoelectric effect does not depend on the amplitude of the radiation used. 

 Which best describes the photoelectric effect? 

The Photoelectric Effect

Sketch the interference pattern that results from the diffraction
of electrons passing through two closely spaced slits.

Photons

The energy required to ionize sodium is 496 kJ/mol. What minimum
frequency of light is required to ionize sodium?

The work function of cesium metal is 188 kJ/mol, which corresponds to light with a wavelength of 637 nm. Which of the following will cause the smallest number of electrons to be ejected from cesium?
(a) High-amplitude wave with a wavelength of 500 nm 
(b) Low-amplitude wave with a wavelength of 500 nm 
(c) High-amplitude wave with a wavelength of 650 nm 
(d) Low-amplitude wave with a wavelength of 650 nm

Cesium metal is frequently used in photoelectric cells because the amount of energy necessary to eject electrons from a cesium surface is relatively small—only 206.5 kJ/mol. What wavelength of light in nanometers does this correspond to?

The amount of energy necessary to remove an electron from an atom is a quantity called the ionization energy, Ei. This energy can be measured by a technique called photoelectron spectroscopy, in which light of wavelength l is directed at an atom, causing an electron to be ejected. The kinetic energy of the ejected electron (Ek) is measured by determining its veloc-ity, v (Ek = mv2/2), and Ei is then calculated using the conservation of energy principle. That is, the energy of the incident light equals Ei plus Ek. What is the ionization energy of selenium atoms in kilojoules per mole if light with l = 48.2 nm produces electrons with a velocity of 2.371 * 106 m/s? The mass, m, of an electron is 9.109 * 10-31 kg.

Molybdenum metal must absorb radiation with an energy
higher than 7.22 * 10-19 J (“energy threshold”) before it can
eject an electron from its surface via the photoelectric effect.
(a) What is the frequency threshold for emission of electrons?

An ultraviolet photon with a wavelength of 320 nm strikes a metal surface. The emitted electron has a kinetic energy of 1030 eV. What is the binding energy of the electron in kJ/mol? 1 electron volt (eV) = 1.602 x 10-19 J.

An argon ion laser puts out 5.0 W of continuous power at a
wavelength of 532 nm. The diameter of the laser beam is
5.5 mm. If the laser is pointed toward a pinhole with a diameter
of 1.2 mm, how many photons travel through the pinhole
per second? Assume that the light intensity is equally
distributed throughout the entire cross-sectional area of the
beam. (1 W = 1 J/s)

Wave-Particle Duality and the Photoelectric Effect

Which type of electromagnetic radiation will cause the greatest number of electrons to be ejected from zinc metal with a work function of 350 kJ/mol? (LO 5.4, 5.5)
(a) Dim light with a wavelength of 320 nm 
(b) Dim light with a wavelength of 360 nm 
(c) Bright light with a wavelength of 360 nm 
(d) Bright light with a wavelength of 375 nm

Photoelectric Basics

Molybdenum metal must absorb radiation with an energy 
higher than 7.22 * 10-19 J (“energy threshold”) before it can 
eject an electron from its surface via the photoelectric effect. 
(b) What wavelength of radiation will provide a photon of this 
energy?

Photoelectric Effect Example 1

Wave-Particle Duality of Light

A minimum energy of 7.21 * 10-19 J is required to produce the photoelectric effect in chromium metal. 
(a) What is the minimum frequency of light needed to remove an electron from chromium?

The work function of silver metal is 436 kJ/mol. What frequency of light is needed to eject electrons from a sample of silver?

Molybdenum metal must absorb radiation with an energy
higher than 7.22 * 10-19 J (“energy threshold”) before it can
eject an electron from its surface via the photoelectric effect.
(c) If molybdenum is irradiated with light of wavelength
of 240 nm, what is the maximum possible velocity of
the emitted electrons?

The work function of calcium metal is kJ/mol, which corresponds to light with a wavelength of 432 nm. Which of the following will cause the largest number of electrons to be ejected from cesium?
(a) High-amplitude wave with a wavelength of 400 nm 
(b) Low-amplitude wave with a wavelength of 400 nm 
(c) High-amplitude wave with a wavelength of 450 nm 
(d) Low-amplitude wave with a wavelength of 450 nm

 The emission of electrons depends on the energy of a single photon. 

 In order to meet the threshold frequency requirement, the photon must have the same or greater energy than the electron's binding energy. 

 The kinetic energy of the ejected electron equals the energy of the photon minus the binding energy of the electron. 

 The excess energy of the photon, beyond the binding energy, is transferred to the electron in the form of kinetic energy. 

 The photoelectric effect is observed when electromagnetic radiation of certain frequency shines on a metal surface.  

 Which of the following is true about the photoelectric effect? 

Photoelectric Effect Example 2

Einstein’s 1905 paper on the photoelectric effect was the
first important application of Planck’s quantum hypothesis.
Describe Planck’s original hypothesis, and explain how
Einstein made use of it in his theory of the photoelectric
effect.

A metal with a threshold frequency of 2.15 x 1015 s-1 emits an electron with a velocity of 7.03 x 106 m/s when radiation of 1.88 x 1015 s-1 strikes the metal’s surface. Calculate the mass of the electron.

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1. Intro to General Chemistry

2. Atoms & Elements

3. Chemical Reactions

4. BONUS: Lab Techniques and Procedures

5. BONUS: Mathematical Operations and Functions

6. Chemical Quantities & Aqueous Reactions

7. Gases

8. Thermochemistry

10. Periodic Properties of the Elements

11. Bonding & Molecular Structure

12. Molecular Shapes & Valence Bond Theory

13. Liquids, Solids & Intermolecular Forces

14. Solutions

15. Chemical Kinetics

16. Chemical Equilibrium

17. Acid and Base Equilibrium

18. Aqueous Equilibrium

19. Chemical Thermodynamics

20. Electrochemistry

21. Nuclear Chemistry

22. Organic Chemistry

23. Chemistry of the Nonmetals

24. Transition Metals and Coordination Compounds

[BOOK CHEM] Clutch Version

Wavelength and Frequency

Wavelength&nbsp;is the distance from one crest of a wave to another, whereas frequency is the number of waves within a second.&nbsp;

Quantum Numbers: Spin Quantum Number

The Spin Quantum Number deals with the spin of an electron within an orbital.

Speed of Light

The Speed of Light in a vacuum is related to the wavelength and frequency of a light particle.

Bohr Equation

In the Bohr Equation, the energy and wavelength a photon is related to its energy shell transitions.

Quantum Numbers: Angular Momentum Quantum Number

The&nbsp;Angular Momentum Quantum Number&nbsp;gives the shape of the atomic orbitals.

Emission Spectrum

Emission Spectra is a series of lines formed when emitted light is focused by a slit and passed through a prism. &nbsp;

Introduction to Quantum Mechanics

The 4 Quantum Numbers provide us the coordinates to find the theoretical location of an electron.

Quantum Numbers: Nodes

A node is the region in an atom with zero electron density and where an electron is least likely to exist.

The Energy of Light

The Energy of Light&nbsp;involves the use of a new variable Planck's Constant.

Electromagnetic Spectrum

The Electromagnetic Spectrum is the different forms of radioactive energy that exists in our universe.

Heisenberg Uncertainty Principle

Heisenberg's Uncertainty Principle&nbsp;tries to explain the potential duality of an electron behaving as either a particle or wave.&nbsp;

Quantum Numbers: Number of Electrons

The Quantum Numbers can give both the quantity and location of electrons within a given atom.&nbsp;

Quantum Numbers: Principal Quantum Number

The Principal Quantum Number gives both the size and energy of an electron shell.&nbsp;

What happens when light strikes the surface of a metal? The Photoelectric Effect&nbsp;can help to explain that.&nbsp;

Quantum Numbers: Magnetic Quantum Number

The Magnetic Quantum Number gives the location of an electron within a specific orbital.

Bohr Model

In the Bohr Model, electrons can move up and down to different orbitals or shells based on absorbing or releasing of energy.&nbsp;

De Broglie Wavelength

The&nbsp;De Broglie Wavelength equation relates wavelength to velocity or speed.&nbsp;