Quanta and Waves

Question 1

What is the y value when calculating the maximum Kinetic energy?

Answer 1

y=0, Ekmax=1/2 m ω^2 A^2

Question 2

Define Simple Harmonic motion

Answer 2

The oscillating motion of an object such that the acceleration of the object is directly proportional to and in the opposite direction to the displacement from its rest position.

a ∝ -x

Question 3

Define Period (T) (in seconds)

Answer 3

The time it takes for one wave cycle to complete.

Question 4

What mode must your calculator be in when doing SHM questions?

Answer 4

Radians.

Question 5

What 4 experimental observations cannot be explained by classical physics, but can be explained using quantum theory?

Answer 5

The photoelectric effect.
Black body radiation curves (ultraviolet catastrophe)
The formation of emission and absorption spectra
Electron diffraction

Question 6

Explain this relationship: ΔxΔp≥h/4π

Answer 6

(Heinsberg’s uncertainty principle)
The precise position and momentum of a particle cannot be known simultaneously.

Question 7

Explain this relationship: ΔEΔt≥h/4π

Answer 7

(Quantum tunnelling)
It is not possible to know the lifetime of a quantum particle and the associated energy change simultaneously.

Question 8

What does ‘quantum’ mean?

Answer 8

The minimum amount of any physical property involved in an interaction.

Question 9

What is the lifetime of a quantum particle measured as?

Answer 9

An uncertainty in time

Question 10

Explain what it is meant by Heisenberg’s ‘uncertainty principle’.

Answer 10

It is not possible to measure the position and the momentum of a quantum particle with absolute certainty.

Question 11

What are 7 features of Bohr’s model of an atom?

Answer 11

1. Positively charged central nucleus.
2. Electrons (negatively charged) are in discrete energy levels and do not radiate energy.
3. Electrons are not permitted to exist between these quantised states.
4. When an electron makes a transition from one energy level to another a specific amount of energy is lost or gained.
5. Energy is absorbed or released in the form of a photon of energy.
6. Each line in a spectrum is produced when an electron moves from one energy level to another.
7. The angular momentum of the electrons in these orbits are quantised in units of h/2π

Question 12

How was de Broglie able to explain the stability of the electrons around the atom when classical physics suggested it should emit radiation and its orbit around the nucleus decrease?

Answer 12

When an electron is in one of the allowed orbits it behaves as if it is a standing wave and not a particle experiencing centripetal acceleration, therefore no radiation is emitted.
The radius of the orbit must be such that it allows for a standing wave to be created, hence it is quantised.

Question 13

What did Louis de Broglie suggest in 1923?

Answer 13

Since light had particle-like properties, then maybe nature was dualistic and particles had wave-like properties.
λ=h/p , λ=h/mv

Question 14

What is it meant by ‘quantum tunnelling?’

Answer 14

A quantum particle can exist in a position that, according to classical physics, has insufficient energy to occupy.

Question 15

What is an example of quantum tunnelling?

Answer 15

Alpha decay.
According to classical physics there should not be enough energy available to cause an alpha emission from a radioactive nucleus
Quantum mechanics shows that an alpha particle can borrow enough energy to tunnel out of the unstable nucleus in a very short lifetime.

Question 16

Explain Electron Diffraction

Answer 16

Electrons are accelerated by an electric field (high voltage)
The fact that they can be accelerated by an electric force shows that they are particles (F=ma)

Electrons then pass through a carbon grid and produce an interference pattern on a phosphor screen.
This shows that electrons are behaving like waves!

Question 17

Describe the double slit experiment and it’s findings.

Answer 17

If electrons are fired at a double slit then an interference pattern is observed! Electrons are behaving like waves.
An interference pattern is still created over time when one electron is fired at a time.
By simply observing what slit the electron actually went through, the electron went back to behaving like a particle, and two fringes were produced!
The de Broglie interpretation is that the electron goes through both slits simultaneously as its wavelength is similar in size to the slit separation. (de Broglie wavelength)

Question 18

Describe what is observed when the ‘photoelectric effect’ occurs.

Answer 18

Electrons are ejected or freed from a metal when it absorbs energy from photons of light.
Evidence for wave-particle duality.

Question 19

What is the photoelectric effect?

Answer 19

The photoelectric effect is when electromagnetic radiation is directed at a metal surface and ejects electrons from the surface.

Question 20

What is the ‘ultraviolet catastrophe’?

Answer 20

Predictions of the shape of the graph of black body radiation using classical theory worked at longer wavelengths but tended to infinity (infinite energy) at shorter wavelengths (ultraviolet).
It took Planck and Einstein using the idea of “quanta” of energy to explain the observed shape of the curve of the spectrum of light radiated by hot objects. (E=nhf)

Question 21

What is the evidence that classical physics cannot account for the photoelectric effect?

Answer 21

If light was a continuous wave motion the electrons would absorb energy continuously and the effect would occur for all frequencies. There would be a time delay till the electrons had absorbed sufficient energy with lower frequencies. To deliver enough energy to the metal the light must occur as small bursts of wave energy.

Question 22

Describe what is meant by ‘cosmic rays’.

Answer 22

Cosmic rays are energetic subatomic particles which arrive in the Earth’s atmosphere from outer space.

Question 23

What is solar wind composed of?

Answer 23

Charged particles in the form of plasma.

Question 24

Explain why charged particles entering Earth’s magnetic field follow a helical motion.

Answer 24

If a charged particle crosses the magnetic field at an angle then only a component of its velocity be perpendicular to the magnetic field. The perpendicular component, (v sin) provides the centripetal force which produces the circular motion. The component of velocity (v cos) parallel to the magnetic field causes no change in the particles motion but it continues to move in that direction in a helical path.

Question 25

What happens when cosmic rays interact with Earth’s atmosphere?

Answer 25

When they arrive at Earth, they collide with the nuclei of atoms in the upper atmosphere, creating more particles, mainly pions.
The charged pions can swiftly decay, emitting particles called muons.
Unlike pions, these do not interact strongly with matter, and can travel through the atmosphere to penetrate below ground.
The rate of muons arriving at the surface of the Earth is such that about one per second passes through a volume the size of a person’s head.
These particles are called a cosmic air shower.

Question 26

What is it meant by damping?

Answer 26

An oscillating system will lose energy to frictional forces such as air resistance. These are known as damping forces and they are often deliberately introduced to reduce the motion of the system.

Question 27

What does underdamped look like graphically?

Answer 27

The amplitude decreases slowly with time.

Question 28

What does critical damping look like graphically?

Answer 28

Critical damping causes a system’s amplitude to reach zero in the shortest time possible.

Question 29

What does over damped look like graphically?

Answer 29

Over damping does not oscillate but moves slowly until coming to a rest.

Question 30

Explain, in terms of the Heisenberg uncertainty principle, why alpha emission is possible from the uranium-235 nucleus.

Answer 30

The momentum of the alpha particle is known precisely therefore its position is not known precisely there is a (small) probability that the particle could exist outside the nucleus (even although classically it does not have sufficient energy to escape).

Question 31

State what is meant by plane‐polarised light.

Answer 31

Light oscillates in a single plane.

Question 32

Why can sound waves not be polarised?

Answer 32

Sound waves are not transverse waves

Question 33

What is unpolarised light?

Answer 33

Light oscillates in many planes.

Question 34

For SHM, what value is y at max speed?

Answer 34

0

Question 35

State what it is meant by ‘coherent waves’

Answer 35

Waves have a constant phase relationship.

Question 36

If a wave travels in a less dense medium and reflects from an interface with a more dense medium, what phase change occurs?

(Less dense to more dense medium)

Answer 36

Phase change of π radians

Question 37

A wave is travelling in a more dense medium and reflects from an interface with a less dense medium.
Does a phase change occur?

More dense medium to less dense medium

Answer 37

No

Question 38

How are stationary waves formed?

Answer 38

The incident and reflected waves interfere. (sound waves)
or
Waves reflected from each end interfere. (string)

Constructive inteference, same amp + frequency, travelling opposite ways