Topic 12 Flashcards
Definition: Gravitational field
A region in space where mass experiences a force.
Equation: Gravitational field strength (uniform field) *
g = F / m
g = gravitational field strength (N kg⁻¹)
F = force (N)
m = mass (kg)
Definition: Gravitational field strength
The gravitational force per unit mass at a point in the field.
(N kg⁻¹)
What is an approximation of a uniform gravitational field?
The field near the surface of a planet or star.
Definition: Gravitational potential Vgrav
The gravitational potential energy per unit mass.
(J kg⁻¹)
Equation: Gravitational potential (uniform field)
ΔVgrav = gΔh
ΔVgrav = change in gravitational potential (J kg⁻¹)
g = gravitational field strength (N kg⁻¹)
Δh = change of height (m)
Equation: Newton’s Law of gravitation *
Fgrav = Gm1m2 / r2
Fgrav = gravitational force between two objects (N)
G = gravitational constant (6.67x10⁻¹¹ Nm²kg⁻²)
m1 = mass of first object (kg)
m2 = mass of second object (kg)
r = distance between two masses (m)
What is the connection between the gravitational force exerted by ‘the moon on the earth’ and ‘the earth on the moon’?
The gravitational force is equal regardless of differences in size or mass.
Equation: Gravitational field strength (around a point mass) *
g = Gm / r2
g = gravitational field strength (N kg⁻¹)
G = gravitational constant (6.67x10⁻¹¹ Nm²kg⁻²)
m = mass of point mass (kg)
r = distance between the two mass (m)
NOTE: r = radius of point mass if working out field strength at surface.
What are the assumptions made using ‘g=Gm/r2’?
The mass being acted upon by gravity is negligible compared to the mass of the point mass.
What is the variation of gravitational field strength due to the Earth?
Equation: Gravitational potential (radial field) *
Vgrav = -GM / r
Vgrav = gravitational potential (J kg-1)
G = gravitational constant (6.67x10⁻¹¹ Nm²kg⁻²)
M = mass of point mass (kg)
r = distance between masses (m)
NOTE: r = radius of point mass if working out field strength at surface.
What assumptions are made using gravitation equations?
That the value is being measured outside of the surface of the mass.
Equation: Gravitational potential energy (radial field)
GPE = -GMm / r
GPE = gravitational potential energy (J)
G = gravitational constant (6.67x10⁻¹¹ Nm²kg⁻²)
M = mass of point mass (kg)
m = mass of orbiting mass (kg)
r = distance between masses (m)
Why do you have to use different equations for uniform and radial fields?
Because gravitational field strength isn’t constant in radial fields.
What happens as a mass moves towards a planet?
It’s GPE decreases and work is done against it by the gravitational field.
What is the relationship between ΔGPE and ΔVgrav?
ΔGPE = ΔVgrav x mass
How does energy change as the radius of an orbit decreases?
- Ek increases, GPE decreases
- Overall energy decreases due to losses in heat.
Equation: Orbits
m2v2 / r = m2rω2 = Gm1m2 / r2
m2 = mass of object in orbit (kg)
v = orbital velocity (ms-1)
r = radius of orbit (m)
ω = angular velocity (rad s-1)
G = gravitational constant (6.67x10⁻¹¹ Nm²kg⁻²)
m1 = mass of planet (kg)
What is the relationship between Fgrav and Fcentripetal which allows us to derive the orbital law?
Fgrav = Fcentripetal
⇒ m2rω2 = Gm1m2 / r2
How is an object kept in orbit?
It experiences a gravitational force which provides a centripetal force.
Equation: Mass-energy *
ΔE = c2Δm
ΔE = change in energy (J)
c = speed of light (3.00x108 ms-1)
Δm = change in mass (kg)
Equation: Atomic mass units *
u = 1.66 x 10-27kg
This is approximately equal tot he mass of a proton/neutron.
Definition: Binding energy
The energy needed to split the nucleus into individual nucleons and move them apart.
How is binding energy affected by nuclei size?
As the size of the nuclei increases, the total binding energy of a nucleus also increases.
What are the sources of background radiation?
- Radon.
- Medical radiotherapy.
- Gamma rays from ground / buildings.
- Food and drink.
- Cosmic.
Equation: Count rate of source
Count rate (of source) = Measured count rate - background count rate
Definition: Ionising power
How many ions are produced per unit distance in a particular material.
Definition: Penetrating power
How far radiation can travel through various materials and what thickness of a particular material is needed to absorb them.
Features: Alpha radiation
Low penetrating power (Paper / skin)
High ionising power
Small range in air (0.02-0.03m)
Features: Beta radiation
Medium penetrating power (thin aluminium)
Medium ionising power
Medium range in air (1-2m)
Features: Gamma radiation
High penetrating power (lead)
Low ionising power
Large range in air (barely absorbed)
Alpha particles
A helium nucleus.
4He24α2
Charge = +2e
Beta particles
A high energy electron.
<span>0 </span>β -1
Charge = -1e
Gamma radiation
An EM photon (of very short wavelength).
<span>o</span>γo
Charge = 0
Mass = 0
Conservation laws of nuclear transformations
- Conservation of baryon number.
- Conservation of charge.
- Conservation of leptop number.
What is a feature of gamma decay?
The structure of the nucleus is not changed, it just removes energy.
Definition: Random decay
We cannot predict which nucelus will be next to decay.
Definition: spontaneous decay
WE cannot influence the decay of radioactive nuclei.
Definition: Half life
The time taken for half of the unstable nuclei to decay.
The time taken for the activity of a sample to half.
Definition: Activity
The number of decays per second in an isotope.
(Bq)
Equation: Activity *
A = dN / dt = -λN
A = activity (Bq)
N = number of nuclei
λ = decay constant
Equation: Half life *
t1/2 = <span>ln2</span>/λ
t1/2 = half life (s)
λ = decay constant
Equation: Radioactive decay *
N = Noe-λt
A = Aoe-λt
N = number of nuclei
No = initial number of nuclei
λ = decay constant
t = time
What do you need to take in to account when discussing dangers of radiation to body?
- Will activity change over the time you are in contact with source?
- Is this type of radiation able to penetrate the body or does it have to be inhaled?
- How ionising is this type of radiation?
- How long is the half life?
- If it does get in the body it could damage your cells.
When is alpha radiation dangerous?
Alpha particles are unable to penetrate the body so are only dangerous if they are inhaled. Once inhaled, they may damage your cells.
Why do nuclei recoil when they emit particles?
Because momentum must be conserved.
What is a radioactive atom?
An atom which has an unstable nucleus and emits alpha, beta or gamma radiation.
<span>23</span>Fb18
23 = proton + neutron number
18 = proton number
neutron number = 23 - 18 = 5
What is a feature of positron emission?
It increases the number of neutrons in nucleus.
How do you increase the accuracy of count rates?
Record the count for a longer time as decay is random.
What are the features of fusion?
The binding energy per nucleon increases.
Total mass decreases.
What are the features of fission?
The binding energy per nucleon increases.
Total mass decreases.
Number of free neutrons increases
How does fusion release energy?
Small nuclei fuse together to produce a larger nucleus. During this process the mass decreases and so according to ΔE = c2Δm energy is released.
What are the conditions needed for fusion?
Very high temperatures to overcome the repulsion between nuclei.
Very high density to maintain a high collision rate.
Why can fusion only produce elements up to iron?
Because the binding energy per nucleon decreases for larger elements and so would require a net input of energy to produce them.
What is the process of nuclear fission?
A large nucleus collides with a neutron and becomes unstable, splitting into two smaller nuclei. Some neutrons are also emitted which go on to cause further fissions in a chain reaction.
How does fission release energy?
Large nucleus splits into smaller nuclei, with an overall decrease in mass. Also, the binding energy per nucleon increases. Therefore, due to ΔE = c2Δm, energy is released.
Why is fusion safer than fission?
Fission reactors produce more radioactive waste and are harder to control.
Why is fusion more sustainable than fission?
Fuel for fission is a limited resource, whereas fuel for fusion is virtually unlimited.
Why is it hard to sustain a contolled fission reaction?
Extremely large temperatures and densities need to be maintained.
