7.2 - The quantum nature - questions

1 - What is the value of Planck's constant ?

2 - What is a photon ?

3 - What is the velocity of a photon ?

4 - How can one calculate the wavelength of a particle if one knows its frequency ?

5 - What is the formula for the energy of a photon ?

6 - What is the formula for the momentum of a photon ?

7 - How does the energy of light depend on the intensity of the light ?

8 - What is relativistic mass ?

9 - What is mass of a photon ?

10 - What is Einstein's famous formula and what does it mean ?

11 - What is the photoelectric effect ? What is its formula ? Draw curve !

12 - Draw a picture and explain the zinc plate experiment.

13 - Describe Millikans photo electric experiment.

14 - Explain why atoms can only send out photons with certain fixed energy (or frequency) ?

15 - An electron jumps between energy levels at -4 and -10 eV. What is the frequency of the light that is created ?

7.3 - The wave nature - questions

16 - Explain how an electron gun works.

17 - What is the de Broglie hypothesis ?

18 - What is the formula for the momentum of an electron according to de Broglie hypothesis ?

19 - What is the formula for the energy of an electron that is non-relativistic (do not travel close to the speed of light) ?

20 - An electron is accelerated with a potential that is 1000 V, what is the energy in Joule ?

21 - What sort of experiments can be done to verify the de Broglie hypothesis ?

22 - What is Heisenberg's uncertainty principle ?

23 - The momentum of a particle is known with a precision of 1 kgm/s. With what precision can one know the position ?

7.4 - The quantum model - questions

24 - Explain the "electrons in a box" model of an atom.

25 - Explain the Schrödinger model of an atom.

26 - If the radius of an atom is 10-10 m then what is the electron wavelength according to the Schrödinger model ?

27 - Fill in this table:

28 - What states can the electron in an atom be in according to the Schrödinger model ?



7.2 - The quantum nature

Look at the data booklet:  

A photon is a packet (or a quantum) of an electromagnetic wave. Depending on the frequency of the wave the photon can be visible light, gamma rays or radio waves.

Look at the data booklet:  

The speed of photons (c) is always the same but light travels slower in a medium such a glass because then photons are absorbed by glass atoms and then emitted again and this process takes time.

Look at the data booklet:  

The velocity in this formula is c for photons i.e. change v to c in the formula when you work with photons.

So for photons one has that:

c = f λ

Look at the data booklet:  

Where E is the energy of the photon and f the frequency of the photon and h is a constant called Planck's constant.

Look at the data booklet:  

Since

c = f λ

and

E = h f

this means that

E = p c

The energy of photons do not depend on the intensity. That means that the photons in bright light has the same energy as photons in dim light. So in bright light you have many more photons but the individual photons do not have more energy.

Since E=hf, the energy of photons only depends on their frequency. This means that for example blue light has photons with larger energy that red light.

When a particle is standing still it has a mass called its rest mass. But when a particle travels very fast (close to the speed of light) its mass gets larger and this larger mass is called its relativistic mass. This mass depends on the particle's energy and it can be anything while the rest mass is a constant value.

The rest mass of photons is zero but since photons are never at rest (they always move at the speed of light) they have a relativistic mass that depends on their energy.

Look at the data booklet:  
E: Energy in J
m: mass in kg
c: speed of light m/s (a constant = 300000 km/s)

The formula tells us that energy is equivalent to mass.

One has to be careful with this formula because for a particle that moves slowly or is standing still, the mass (m) in the formula is the rest mass of the particle. But for a particle that is moving fast, such as a photon, m is the relativistic mass (mrel) and not the rest mass (mo).


1. The photoelectric effect is when photons (for example light photons) kicks out electrons from a plate.

2. These electrons are called photoelectrons. All of the energy of the photon is transferred to the electron and the photon therefore disappears.

3. The energy of the electron depends on the energy of the photon and since Ephoton = h•f= h•c/λ this means that it depends on the frequency or wavelength of the light.

4. A minimum photon energy, called the threshold energy (φ = hfo) is needed to kick out an electron. This means that the photons needs a minimum threshold frequency (fo) to kick out the electrons. If the photon energy (or frequency) is larger than the threshold energy the remaining energy is given as kinetic energy to the electrons (E). Emax is the largest energy that the photons can get since some of the photon energy can also be lost on other things.

Look at the data booklet:  

And re-arrange it to get     Emax = hf - hfo


1. Charge up a Zink plate with an electroscope so that it is negatively charged.
2. The leafs on the electroscope will then repel each other because of the extra electrons.
3. When light with high enough energy ( = frequency), for example ultra-violet light, hits the Zink plate, the electroscope loses charge because electrons are kicked out and the leafs starts to fall.
4. If the intensity of the light is increased, more electrons will be kicked out and the leaf will fall quicker.
5. However, if the frequency of the light is lowered to red light, nothing will happen because the photon energy is not high enough to kick out electrons.



V = 0

Light hits the photosurface and kick out electrons that creates a current.
The normal formula for photoelectric effect can be used: Emax = hf - hfo

V > 0

The positive voltage will attract the electrons and the current will increase with increasing V.
The maximum current depends on how bright the light is (its intensity).

V < 0

A negative voltage will repel the electrons.
The larger the negative voltage the more we repel the electrons and the more the current goes down.

V = Vs

When the current is zero, the voltage is called Vs.
This voltage can be used to calculate the minimum threshold frequency (fo) that the photons needs to have to kick out electrons.
Look at the data booklet:       where
hf0 = hf - eV = The minimum photon energy needed to kick out an electron.
hf = The energy of the incoming photons.
e = The elementary charge = 1.60x10-19C (see databooklet).
V = The voltage needed to make the current zero.




1. The electrons in an atom shell can only be in certain energy levels.
2. Photons are emitted (or absorbed) when electrons move between energy levels.
3. The difference between the energy levels give the energy of the photons.

ΔE = hf

where ΔE is the difference between two electron energy levels and f is the frequency of the photon.

An electron jumps between energy levels at -4 and -10 eV. What is the frequency of the light that is created ?

7.3 - The wave nature


1. The hot filament liberates electrons.
2. The electrons are accelerated by the potential towards the anode.
3. The electrons goes through a hole in the anode with a kinetic energy that is V•e.
4. So the electron's energy in units of eV is given by the voltage. If the voltage is 200V the energy of one electron is 200 eV.

The de Broglie hypothesis

1. All particles have an associated wavelength.

2. The wavelength is given by λ = h / p where h is Planck's constant and p is the momentum of a particle.

Look at the data booklet:  

Look at the data booklet:  

So for particles such as the electron the momentum is:

p = m v = h / λ

where m is the relativistic mass if the particle has a speed close to the speed of light. Otherwise it is the restmass of the particle.

Look at the data booklet:  

Look at the data booklet:  

1000 V means that the energy is 1000 eV.

The energy in Joule is then 1000•1.6 x 10-19

If electrons from an electron gun are passed through a thin film of graphite one can see diffraction patterns on a phosphor screen.

One can also reflect electrons off a nickel crystal (Davidson-Germer experiment). The reflected electrons then show a diffractive pattern.

You only get these diffractive patterns because the electrons acts like waves.

Look at the data booklet:  

Look at the data booklet:  
Δp : The precision (error) of a measurement of momentum
Δx : The precision (error) of a measurement of position
ΔE : The precision (error) of a measurement of energy
Δt : The precision (error) of a measurement of time

Heisenberg's uncertainty principle says that one cannot measure momentum and position of a particle (or energy and time) to any precision. There is a limit to how well one can know these things.

The momentum of a particle is known with a precision of 1 kgm/s. With what precision can one know the position ?

Δx > h / (4πΔp) = 6.63•10-34/4π = 0.5•10-34 m since Δp = 1 kgm/s

7.4 - The quantum model

If one regards the electrons in an atom as a wave trapped in a box of length L one can show that the kinetic energy Ek of the electrons can only take some values that depend on a number n that give the number of nodes of the wave.

Look at the data booklet:  

The "electrons in a box" model does not give the correct energy levels but the Schrödinger model does. It says that the electron can be described by a wave function (ψ) and that the square of the wave function (ψ2) is giving the probability of finding the electron at a certain location in space. So the model predicts that the electrons can only have certain fixed levels but that the position is not fixed. The electrons are like clouds around the nucleus.

If the radius of an atom is 10-10 m then the electron wavelength also has to be about 10-10 m according to the Schrödinger model.

1. The model assumes that electrons are described by wavefunctions.
2. The wave associated with the electrons are bounded by the atom.
3. This means that if the size of the atom is 10-10 m then the wavelength is the same.



There are 4 numbers that define the position of an electron. It can be thought of the telephone number of an electron.

The first number is called the principal quantum number(n). Its range is any natural number.

The second number is the azimuthal quantum number (l) , this determines the shape of the orbital. Its range is dependent on n and is (0,n-1).

The third number is the magnetic quantum number (ml), it tells us the direction that the orbital is pointing (eg. it will differentiate between a p-orbital along the x-axis and a p-orbital along the y-axis) ml can take values from -l to l.

Finally, there is the electron spin which have a spin quantum number (ms) which cane have the two values +1/2 and -1/2.