Modern Physics Notes
Stephen Thomspon
February 2023
1 Lecture 1: The backbone of theories through-
out time
This is the beginning of a large topic. This will span throughout the second
semester of the first year covering half of the Newton to Einstein lectures. To
start with we must cover the foundations of modern physics. Therefore, let
us begin with the basics. By the early 19th century scientists believed light
traveled as a wave due to the interference in Young’s Double slit experiment.
Furthermore, they knew of the presence of atoms due to anode-cathode cells
being set up.
Let us move onto light as an emission spectrum. A diffraction grating will
split the light into its constituent wavelengths. Typically heated solids emit a
continuous spectrum but gases only emit certain discrete wavelengths. Let us
do a deeper dive into continuous spectra. Consider the general curve for a black
body, for the intensity against wavelength. Now let us consider discrete spectra.
Similarly, a diffraction grating can also be used to measure the diffraction of a
gas. Gases are only able to absorb certain discrete wavelengths which are the
subset of the emission wavelengths.
Now we move on to the oil drop experiment which allowed the first calculations
of the elementary charge.
This concludes the main details of the lecture the rest are elementary and
do not need to be repeated.
2 Lecture 2: Photoelectric Effect
Phillip Lenard’s experiment of the cathode ray tube gave us a handful of ob-
servations to try and explain. The first of which is the current is proportional
to the intensity of light. Secondly, the current flows with no delay. The current
will only be induced if the frequency of light is above the threshold frequency
and this threshold frequency depends on the material. The current induced will
depend on ∆V . I is constant for ∆V > 0 and I = 0 for ∆V =< −Vstop . Finally,
the stopping potential (Vstop is independent of the light intensity.
Let us begin to explain these phenomena. To begin this we need to introduce
1
, the work function of a metal. This is the minimum energy (E0 ) to free an elec-
tron from a metal. Now put this into the context of the conservation of energy.
The photon will have a one-to-one interaction with an electron on the metal’s
surface. Therefore, the energy of the photon above the work function will be
converted into the kinetic energy of the electron.
Dependence of current on the potential difference. If ∆v > 0 the positive anode
will attract electrons, most of which will reach the anode. If ∆V = 0 electrons
leave the cathode in all directions, some of which will reach the anode contribut-
ing to the induction of a current. Finally, if ∆V < 0 then the negative anode
repels electrons and only a few reach the anode. Now let us introduce the idea
of a stopping potential, which is given by the expression:
Kmax
Vstop = (1)
e
Now we can move on to the quantization of photons. According to Max Planck,
you can only have amplitudes such that energy is an integer number times
Planck’s constant. This progressed in 1905 when Einstein proposed the photo-
electric effect, light travels as photons with energy:
E = hf (2)
Light can only be emitted and absorbed in discrete quanta and when absorbed
by a metal each photon gives all of its energy to one electron. We can use this
to further define the stopping potential as:
hf − E0
Vstop = (3)
e
This shows that the energy is independent of the intensity of light as that
describes the number of photons not the energy of a singular photon. This
concludes the second lecture in this series and will be followed by the next
lecture which looks deeper into photons and quantization.
3 Lecture 3: Photons and quantization
The start of this lecture is concerned with light behaving like particles and waves
however, this is elementary knowledge so it needs to be covered again refer to
notes in the lecture. To start we will look at other particles behaving like waves
so let us recall from relativity, that the energy of a particle can be found from
the expression:
E 2 = (pc)2 + (mc2 )2 (4)
Now we can substitute the mass of the photon to be zero. This leaves us with
the energy being:
E = pc (5)
2
Stephen Thomspon
February 2023
1 Lecture 1: The backbone of theories through-
out time
This is the beginning of a large topic. This will span throughout the second
semester of the first year covering half of the Newton to Einstein lectures. To
start with we must cover the foundations of modern physics. Therefore, let
us begin with the basics. By the early 19th century scientists believed light
traveled as a wave due to the interference in Young’s Double slit experiment.
Furthermore, they knew of the presence of atoms due to anode-cathode cells
being set up.
Let us move onto light as an emission spectrum. A diffraction grating will
split the light into its constituent wavelengths. Typically heated solids emit a
continuous spectrum but gases only emit certain discrete wavelengths. Let us
do a deeper dive into continuous spectra. Consider the general curve for a black
body, for the intensity against wavelength. Now let us consider discrete spectra.
Similarly, a diffraction grating can also be used to measure the diffraction of a
gas. Gases are only able to absorb certain discrete wavelengths which are the
subset of the emission wavelengths.
Now we move on to the oil drop experiment which allowed the first calculations
of the elementary charge.
This concludes the main details of the lecture the rest are elementary and
do not need to be repeated.
2 Lecture 2: Photoelectric Effect
Phillip Lenard’s experiment of the cathode ray tube gave us a handful of ob-
servations to try and explain. The first of which is the current is proportional
to the intensity of light. Secondly, the current flows with no delay. The current
will only be induced if the frequency of light is above the threshold frequency
and this threshold frequency depends on the material. The current induced will
depend on ∆V . I is constant for ∆V > 0 and I = 0 for ∆V =< −Vstop . Finally,
the stopping potential (Vstop is independent of the light intensity.
Let us begin to explain these phenomena. To begin this we need to introduce
1
, the work function of a metal. This is the minimum energy (E0 ) to free an elec-
tron from a metal. Now put this into the context of the conservation of energy.
The photon will have a one-to-one interaction with an electron on the metal’s
surface. Therefore, the energy of the photon above the work function will be
converted into the kinetic energy of the electron.
Dependence of current on the potential difference. If ∆v > 0 the positive anode
will attract electrons, most of which will reach the anode. If ∆V = 0 electrons
leave the cathode in all directions, some of which will reach the anode contribut-
ing to the induction of a current. Finally, if ∆V < 0 then the negative anode
repels electrons and only a few reach the anode. Now let us introduce the idea
of a stopping potential, which is given by the expression:
Kmax
Vstop = (1)
e
Now we can move on to the quantization of photons. According to Max Planck,
you can only have amplitudes such that energy is an integer number times
Planck’s constant. This progressed in 1905 when Einstein proposed the photo-
electric effect, light travels as photons with energy:
E = hf (2)
Light can only be emitted and absorbed in discrete quanta and when absorbed
by a metal each photon gives all of its energy to one electron. We can use this
to further define the stopping potential as:
hf − E0
Vstop = (3)
e
This shows that the energy is independent of the intensity of light as that
describes the number of photons not the energy of a singular photon. This
concludes the second lecture in this series and will be followed by the next
lecture which looks deeper into photons and quantization.
3 Lecture 3: Photons and quantization
The start of this lecture is concerned with light behaving like particles and waves
however, this is elementary knowledge so it needs to be covered again refer to
notes in the lecture. To start we will look at other particles behaving like waves
so let us recall from relativity, that the energy of a particle can be found from
the expression:
E 2 = (pc)2 + (mc2 )2 (4)
Now we can substitute the mass of the photon to be zero. This leaves us with
the energy being:
E = pc (5)
2
