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Lesson 2: Exponential Decay and Atom Structure
Lesson 2: Exponential Decay and Atom Structure
What is the purpose of a mass spectrometer?
To determine the mass of a given atom.
What is the equation for magnetic force in terms of magnetic field strength and velocity of an ion?
F = qvB
F = Magnetic Force
q = Charge of ion
V = Velocity of ion
B = Magnetic Field Strength
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In a mass spectrometer, the ion moves in a circle. Why?
The ion moves in a circle because the magnetic force is perpendicular to the velocity of the ion, pointing toward the center of the circle. The magnetic force essentially acts as a centripetal force.
Which equation can be used in tandem with F = qvB in order to calculate the mass of an ion in a mass spectrometer based on the radius of the circle?
Fc = m(v^2/r)
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What is the resulting equation when everything is set equal to r?
r = mv/qB
Of the following ions, which will have the smallest radius in a mass spectrometer?
(A) Carbon-12
(B) Nitrogen-14
(C) Oxygen-16
(D) Potassium-19
(A) Carbon-12
The smaller the mass, the smaller the radius of the circle.
The photoelectric effect describes the phenomenon in which a(n) ________ strikes a metal, resulting in the emission of a(n) ________
(A) Electron, electron
(B) Electron, photon
(C) Photon, photon
(D) Photon, electron
(D) Photon, electron
The photoelectric effect describes the phenomenon in which a photon strikes a metal, resulting the emission of an electron.
The energy of the photon is greater than, equal to, or less than the energy of the emitted electron? Why?
The energy of the photon is greater than the energy of the emitted electron. This is because some of the energy of the photon was required (and used up) in order to free the electron from the metallic surface.
What is the work function?
The work function is the energy of the photon that was required (and used up) in order to free the electron from the metallic surface.
What is the equation for the energy of a photon in terms of the energy of the emitted electron?
KEp = KEe + WF
KEp = Kinetic energy of the photon
KEe = Kinetic energy of the electron
WF = Work function
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A metal has a work function equal to 3.42 ⋅ 10^-19 J and the energy of the electron is equal to 3.47 ⋅ 10^-19 J. What is the frequency of the photon? (remember Plank's constant = 6.626 ⋅ 10^-34).
(A) 3.04 ⋅ 10 ^ -19 Hz
(B) 6.02 ⋅ 10 ^ -13 Hz
(C) 8.06 ⋅ 10 ^ 12 Hz
(D) 1.15 ⋅ 10 ^ 15 Hz
(D) 1.15 ⋅ 10 ^ 15 Hz
KEp = KEe + WF
KEp = 3.47 ⋅ 10^-19 J + 3.42 ⋅ 10^-19 J
KEp = 6.89 ⋅ 10^-19 J
hv = KEp
(6.626 ⋅ 10^-34)v = 6.89 ⋅ 10^-19 J
v = (7 ⋅ 10^-19)/(6 ⋅ 10^-34)
v = about 1 ⋅ 10^15 hz (Actual 1.15 ⋅ 10^15 hz)
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CRB Which physics equation relates the energy of a photon to its frequency?
E = hf
E = Energy of a photon or quantum
h = Planck's Constant (6.626 ⋅ 10^-34 J⋅s)
f = Frequency of wave/radiation
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What two equations can be used in concert with Fc = m(v^2/r) to determine the radius of a Bohr model electron?
Fe = k((q1q2)/r^2) and L = rp
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Based on these equations, what equation can be used to determine the radius of any electron in terms of its principal quantum number?
rn = n^2 r1
rn = Radius of electron at n
n = Principle quantum number
r1 = Radius of electron at n of 1 (5.3 ⋅ 10^-11)
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An electron's total energy is composed of what two types of energy?
(A) Thermal and kinetic energy
(B) Kinetic and electric energy
(C) Electric and potential energy
(D) Thermal and electric energy
(B) Kinetic and electric energy
An electron's total energy is composed of kinetic and electric energy.
What equation can be used to determine the energy of any electron in terms of its principal quantum number?
En = E1/(n^2)
En = Energy of electron at n
n = Principal quantum number
E1 = Energy of electron at n=1 (-2.17 ⋅ 10^-18 J)
Which of the following is the conversion factor from Joules to electron-Volts (eV)?
(A) 1 eV = 6.626 ⋅ 10^-34 J
(B) 1 eV = 1.6 ⋅ 10^-19 J
(C) 1 eV = 3 ⋅ 10^8 J
(D) 1 eV = 9.11 ⋅ 10^-31 J
(B) 1 eV = 1.6 ⋅ 10^-19 J
(A) [6.626 ⋅ 10^-34]is equal to Planck's constant
(C) [3 ⋅ 10^8] is equal to the speed of light
(D) [9.11 ⋅ 10^-31] is equal to the mass of an electron
The energy at the first orbital is equal to -2.17 ⋅ 10^-18 J. What is the energy in terms of electron-volts (eV)?
(A) 19.2 eV
(B) 3.7 eV
(C) -1.4 eV
(D) -13.6 eV
(D) -13.6 eV
(-2.17 ⋅ 10^-18 J) / (1.6 ⋅ 10^-19) = approximately -10 eV (actual: -13.6 eV)
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The energy at the first orbital is equal to -13.6 eV. What is the energy in terms of electron-volts (eV) of an electron in the third orbital?
(A) -9.6 eV
(B) -4.8 eV
(C) -3.4 eV
(D) -1.5 eV
(D) -1.5 eV
En = E1/(n^2)
E3 = -13.6 eV / 3^2
E3 = approx. -1.5 eV
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An electron drops from the second orbital to the first orbital. A photon with how much energy is given off?
(A) -9.6 eV
(B) 6.3 eV
(C) 10.2 eV
(D) 13.6 eV
(C) 10.2 eV
En = E1/(n^2)
E2 = -13.6 eV / 2^2
E2 = approx. -3 eV
E1 - E2 = -13.6 eV - (-3eV) = -10.6 eV from the electron, so the photon has an energy of approx. 10.6 eV (actual: 10.2 eV)
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What does it mean in terms of energy levels of electrons to say that the ionization energy of an atom is -13.6 eV?
It would require 13.6 eV to move an electron from n=1 to n=infinity, making the Hydrogen atom an ion.
CRB Ernest Rutherford conducted an experiment in which he fired alpha particles at gold foil. He noticed that the majority of alpha particles were not deflected by the gold foil, and all alpha particles would exit the foil. What did these results reveal about an atom's structure?
The Rutherford experiments concluded that an atom has a dense, positively charged nucleus taking up a small fraction of an atom's volume.
CRB Which 20th century scientist's theory built upon Rutherford's experiments to develop a Hydrogen atom model, relying on a single electron revolving around a nucleus and only allowing for discrete energy changes between electrons?
(A) Niels Bohr
(B) Richard Feynman
(C) Albert Einstein
(D) John Dalton
(A) Niels Bohr
The Bohr model of an atom relies on an electron revolving around a nucleus and only allowing for discrete energy changes between electrons.
CRB Based on the previous description of the Bohr model, which of the following atoms does not represent the Bohr model?
(A) H
(B) He+
(C) Li+
(D) Be 3+
(C) Li+
The Bohr model relies upon there being only a single electron. Li+ has two electrons, whereas all other options have only one electron.
CRB True or false? Based on the Bohr model, the energy of an orbiting electron is directly proportional to the principal quantum number, with larger principal quantum numbers having less energy.
False. Based on the Bohr model, the energy of an orbiting electron is directly proportional to the principal quantum number, with larger principal quantum numbers having MORE energy.
CRB True or false? The Rydberg unit of energy is equal to 2.18 ⋅ 10 ^-18 J/electron, and is the experimentally determined energy of an electron at the smallest possible orbital.
True. The Rydberg unit of energy is equal to 2.18 ⋅ 10 ^-18 J/electron, and is the experimentally determined energy of an electron at the smallest possible orbital.
CRB Which of the following is not a characteristic of an electron moving from a lower energy orbit to a higher energy orbit?
(A) Emitting light
(B) Increased distance from the nucleus
(C) Excitation of the electron
(D) Increasing potential
(A) Emitting light
An electron moving from a lower energy orbit to a higher energy orbit will ABSORB light, have higher potential, be excited, and increase its distance from the nucleus. Think of the mnemonic "AHED" [Absorb, High potential, Excited, Distant from nucleus] for this!
CRB An atom in the _________ state will emit a photon to release energy and return to the ________ state.
(A) Ground, excited
(B) Excited, ground
(C) Elevated, resting
(D) Resting, elevated
(B) Excited, ground
An atom in the excited state will emit a photon to release energy and return to the ground state.
CRB Based on the Bohr model and the discrete levels of energy electrons can have, what is unique about each element based on electrons returning from the excited to the ground state?
(A) Ground quantum number
(B) Lyman Series
(C) Angular momentum
(D) Atomic emission spectrum
(D) Atomic emission spectrum
Based on the Bohr model and the discrete levels of energy electrons can have, each element will have a unique atomic emission spectrum based on electrons returning from the excited to the ground state.
This also means each element will have a unique absorption spectrum as well.
