Knowt
Unit 7: Quantum, Atomic, and Nuclear Physics
Photons and the photoelectric effect
Quanta: Light being emitted as individual packets of energy called quanta.
Photon: A quantum of electromagnetic energy is known as a photon
Photoelectric effect: light behaves like a stream of photons, and this is
illustrated by the photoelectric effect
Photoelectrons: the released electrons are known as photoelectrons
Wave theory of light predicted three results:
Significant time delay between the moment of illumination and the ejection of photoelectrons.
Increasing the intensity of the light could cause the electrons to leave the metal surface with greater kinetic energy.
Photoelectrons would be emitted regardless of the frequency of the incident energy, as long as the intensity was high enough.
These predictions were not observed.
As, photoelectrons were ejected within a few billionths of a second after illumination, disproving the prediction.
Increasing the intensity of the light did not cause photoelectrons to leave the metal surface with greater kinetic energy.
For each metal there was a certain threshold frequency
E = hf
h is the Planck’s constant = 6.63 x 10^-34 J/s.
Metal’s work function is the certain amount of energy that has to be imparted to an electron on the metal surface
Kmax = hf -ϕ
fo = ϕ/ h
SI unit for energy is the joule
Example
The work function, ϕ, aluminum is 4.08 eV
(a) What is the threshold frequency required to produce photoelectrons from
aluminum?
(b) Classify the electromagnetic radiation that can produce photoelectrons.
(c) If light of frequency f = 4.00 × 1015 Hz is used to illuminate a piece of
aluminum,
(i) what is Kmax, the maximum kinetic energy of ejected photoelectrons?
(ii) what’s the maximum speed of the photoelectrons? (Electron mass = 9.11×
10−31 kg.)
(d) If the light described in part (b) were increased by a factor of 2 in intensity,
what would happen to the value of Kmax?
Solution
The Bohr Model of the atom
The light from a glowing gas, passed through a prism to disperse the beam
into its component wavelengths, produces patterns of sharp lines called
atomic spectra.
R is Rydberg constant = 1.1 x 10^-7
The electron absorbs a certain amount of energy, and it is excited to a higher
orbit, emitting a photon in the process.
The wavelength of the photon
Example
The first five energy levels of an atom are shown in the diagram
below:
(a) If the atom begins in the n = 3 level, what photon energies could be
emitted as it returns to its ground state?
(b) What could happen if this atom, while in an undetermined energy state,
were bombarded with a photon of energy 10eV?
Solution
Wave-Particle Duality
The electromagnetic radiation propagates like a wave but exchanges energy
like a particle. This is known as wave-particle duality.
De-Broglie Wavelength
Example
Electrons in a diffraction experiment are accelerated through a
potential difference of 200 V. What is the de Broglie wavelength of these
electrons?
Solution
The Wave Function
The probability that a particle will be measured to be at a particular position
when the position is measured. That probability is related to a new physical
parameter called the wave function.
Relativity
The Theory of relativity has only two postulates:
The results of physical experiments will be the same in any
non-accelerating reference frames.
The speed of light is constant
Time dilation:
Demonstrated by synchronized atomic clocks.
E.g: When a clock placed on a fast-moving airplane is compared to a clock at rest on the ground, the clock in the airplane shows that less time has passed than the time recorded by the clock on the ground.
This is known as time dilation.
Length Contraction:
To be consistent with time dilation, there must also be disagreement
Nuclear Physics
The nucleus of an atom is composed of particles, protons, and neutrons.
Protons + Neutrons = Nucleons
The number of protons in a given nucleus is called the atom’s atomic number
denoted by Z.
The total number of nucleons (Z+N), is called the mass number, and is
denoted by A.
Isotopes: The nuclei that contain the same numbers of neutrons are called
isotopes
Notation
Example
How many protons and neutrons are contained in the nuclide ?
Solution
The subscript (the atomic number, Z) gives the number of protons, which is
29. The superscript (the mass number, A) gives the total number of nucleons.
Since A = 63 = Z + N, we find that N = 63 − 29 = 34
The Nuclear Force
The strong nuclear force is a fundamental force that binds neutrons and
protons together to form nuclei.
Binding Energy
The masses of the proton and neutron:
Proton: 1.6726 x 10^-27 kg
Neutron: 1.6749 x 10^-27 kg
Mass defect: The difference between the mass of any bound nucleus and the
sum of the masses of its constituent nucleons is called the mass defect.
E = mc^2
Binding energy tells us how strongly the nucleus is bound
Example
What is the maximum wavelength of EM radiation that could beused to photodisintegrate a deuteron?
Solution
The binding energy of the deuteron is 2.23 MeV,
so a photon would need to have at least this much energy
to break the deuteron into a proton and neutron. Since E =
hf and f = c/λ
Nuclear Reactions
Nuclear fusion: It is of small nuclei at extremely high temperatures.
Nuclear fission: The emission of a particle or splitting of the nucleus
Alpha Decay
When a nucleus undergoes alpha decay, it emits an alpha particle, which
consists of two protons and two neutrons.
It is the same as the nucleus of a helium-4 atom.
An alpha particle can be represented as
Two important features of a nuclear reaction:
Mass number is conserved.
Charge is conserved.
The decaying nuclide is known as the parent.
The resulting nuclide is known as the daughter.
Beta Decay
There are three categories of beta decay, called β+, β−, and electron capture.
β− decay:
When the neutron-to-proton ratio is too large, the nucleus undergoes
β− decay.
It occurs when a neutron transforms into a proton and releases an
electron. The expelled electron is called a beta particle.
The transformation of a neutron into an electron and a proton, and
another particle called the electron antineutrino is caused by the
action of weak nuclear force.
β+ decay:
When the neutron-to-proton ratio is too small, the nucleus will undergo
β+ decay.
In this form of β+ decay, a proton is transformed into a neutron and a
positron, and another particle is called electron-neutrino.
Electron Capture:
In which a nucleus can increase its neutron-to-proton ratio to capture
an orbiting electron and then cause the transformation of a proton into
a neutron
Gamma Decay
In each of the decay processes defined above, the daughter was a different
element than the parent. By contrast, gamma decay does not alter the identity
of the nucleus; it just allows the nucleus to relax and shed energy.
It must emit energy in the form of a photon or a gamma ray.
Example
A mercury-198 nucleus is bombarded by a neutron, which causes a
nuclear reaction: What’s the unknown product particle, X?
Solution
In order to balance the superscripts, we must have 1 + 198 = 197 + A, so A = 2, and the subscripts are balanced if 0 + 80 = 79 + Z, so Z = 1:
Conclusion
Disintegration Energy
Nuclear reactions must conserve total energy.
It involves the emission or absorption of energy.
A general nuclear reaction is written as:
A + B —> C + D + Q
Q is disintegration energy
If Q is positive then the reaction is exothermic.
If Q is negative then the reaction is endothermic
Unit 7: Quantum, Atomic, and Nuclear Physics
Photons and the photoelectric effect
Quanta: Light being emitted as individual packets of energy called quanta.
Photon: A quantum of electromagnetic energy is known as a photon
Photoelectric effect: light behaves like a stream of photons, and this is
illustrated by the photoelectric effect
Photoelectrons: the released electrons are known as photoelectrons
Wave theory of light predicted three results:
Significant time delay between the moment of illumination and the ejection of photoelectrons.
Increasing the intensity of the light could cause the electrons to leave the metal surface with greater kinetic energy.
Photoelectrons would be emitted regardless of the frequency of the incident energy, as long as the intensity was high enough.
These predictions were not observed.
As, photoelectrons were ejected within a few billionths of a second after illumination, disproving the prediction.
Increasing the intensity of the light did not cause photoelectrons to leave the metal surface with greater kinetic energy.
For each metal there was a certain threshold frequency
E = hf
h is the Planck’s constant = 6.63 x 10^-34 J/s.
Metal’s work function is the certain amount of energy that has to be imparted to an electron on the metal surface
Kmax = hf -ϕ
fo = ϕ/ h
SI unit for energy is the joule
Example
The work function, ϕ, aluminum is 4.08 eV
(a) What is the threshold frequency required to produce photoelectrons from
aluminum?
(b) Classify the electromagnetic radiation that can produce photoelectrons.
(c) If light of frequency f = 4.00 × 1015 Hz is used to illuminate a piece of
aluminum,
(i) what is Kmax, the maximum kinetic energy of ejected photoelectrons?
(ii) what’s the maximum speed of the photoelectrons? (Electron mass = 9.11×
10−31 kg.)
(d) If the light described in part (b) were increased by a factor of 2 in intensity,
what would happen to the value of Kmax?
Solution
The Bohr Model of the atom
The light from a glowing gas, passed through a prism to disperse the beam
into its component wavelengths, produces patterns of sharp lines called
atomic spectra.
R is Rydberg constant = 1.1 x 10^-7
The electron absorbs a certain amount of energy, and it is excited to a higher
orbit, emitting a photon in the process.
The wavelength of the photon
Example
The first five energy levels of an atom are shown in the diagram
below:
(a) If the atom begins in the n = 3 level, what photon energies could be
emitted as it returns to its ground state?
(b) What could happen if this atom, while in an undetermined energy state,
were bombarded with a photon of energy 10eV?
Solution
Wave-Particle Duality
The electromagnetic radiation propagates like a wave but exchanges energy
like a particle. This is known as wave-particle duality.
De-Broglie Wavelength
Example
Electrons in a diffraction experiment are accelerated through a
potential difference of 200 V. What is the de Broglie wavelength of these
electrons?
Solution
The Wave Function
The probability that a particle will be measured to be at a particular position
when the position is measured. That probability is related to a new physical
parameter called the wave function.
Relativity
The Theory of relativity has only two postulates:
The results of physical experiments will be the same in any
non-accelerating reference frames.
The speed of light is constant
Time dilation:
Demonstrated by synchronized atomic clocks.
E.g: When a clock placed on a fast-moving airplane is compared to a clock at rest on the ground, the clock in the airplane shows that less time has passed than the time recorded by the clock on the ground.
This is known as time dilation.
Length Contraction:
To be consistent with time dilation, there must also be disagreement
Nuclear Physics
The nucleus of an atom is composed of particles, protons, and neutrons.
Protons + Neutrons = Nucleons
The number of protons in a given nucleus is called the atom’s atomic number
denoted by Z.
The total number of nucleons (Z+N), is called the mass number, and is
denoted by A.
Isotopes: The nuclei that contain the same numbers of neutrons are called
isotopes
Notation
Example
How many protons and neutrons are contained in the nuclide ?
Solution
The subscript (the atomic number, Z) gives the number of protons, which is
29. The superscript (the mass number, A) gives the total number of nucleons.
Since A = 63 = Z + N, we find that N = 63 − 29 = 34
The Nuclear Force
The strong nuclear force is a fundamental force that binds neutrons and
protons together to form nuclei.
Binding Energy
The masses of the proton and neutron:
Proton: 1.6726 x 10^-27 kg
Neutron: 1.6749 x 10^-27 kg
Mass defect: The difference between the mass of any bound nucleus and the
sum of the masses of its constituent nucleons is called the mass defect.
E = mc^2
Binding energy tells us how strongly the nucleus is bound
Example
What is the maximum wavelength of EM radiation that could beused to photodisintegrate a deuteron?
Solution
The binding energy of the deuteron is 2.23 MeV,
so a photon would need to have at least this much energy
to break the deuteron into a proton and neutron. Since E =
hf and f = c/λ
Nuclear Reactions
Nuclear fusion: It is of small nuclei at extremely high temperatures.
Nuclear fission: The emission of a particle or splitting of the nucleus
Alpha Decay
When a nucleus undergoes alpha decay, it emits an alpha particle, which
consists of two protons and two neutrons.
It is the same as the nucleus of a helium-4 atom.
An alpha particle can be represented as
Two important features of a nuclear reaction:
Mass number is conserved.
Charge is conserved.
The decaying nuclide is known as the parent.
The resulting nuclide is known as the daughter.
Beta Decay
There are three categories of beta decay, called β+, β−, and electron capture.
β− decay:
When the neutron-to-proton ratio is too large, the nucleus undergoes
β− decay.
It occurs when a neutron transforms into a proton and releases an
electron. The expelled electron is called a beta particle.
The transformation of a neutron into an electron and a proton, and
another particle called the electron antineutrino is caused by the
action of weak nuclear force.
β+ decay:
When the neutron-to-proton ratio is too small, the nucleus will undergo
β+ decay.
In this form of β+ decay, a proton is transformed into a neutron and a
positron, and another particle is called electron-neutrino.
Electron Capture:
In which a nucleus can increase its neutron-to-proton ratio to capture
an orbiting electron and then cause the transformation of a proton into
a neutron
Gamma Decay
In each of the decay processes defined above, the daughter was a different
element than the parent. By contrast, gamma decay does not alter the identity
of the nucleus; it just allows the nucleus to relax and shed energy.
It must emit energy in the form of a photon or a gamma ray.
Example
A mercury-198 nucleus is bombarded by a neutron, which causes a
nuclear reaction: What’s the unknown product particle, X?
Solution
In order to balance the superscripts, we must have 1 + 198 = 197 + A, so A = 2, and the subscripts are balanced if 0 + 80 = 79 + Z, so Z = 1:
Conclusion
Disintegration Energy
Nuclear reactions must conserve total energy.
It involves the emission or absorption of energy.
A general nuclear reaction is written as:
A + B —> C + D + Q
Q is disintegration energy
If Q is positive then the reaction is exothermic.
If Q is negative then the reaction is endothermic
