Binding energy

Question 1

State the main interaction when an alpha particle is scattered by a gold nucleus

Answer 1

EM/electrostatic repulsion between alpha particles and nucleus

Question 2

Explain whether or not the scattering distribution of the monoenergetic alpha particles remains the same when the gold foil is replaced with another foil of the same size made from a mixture of gold isotopes

Answer 2

The scattering distribution remains the same because the alpha particles interact with a nucleus whose charge remains the same

or
less distinct because there is a mixture of nuclear masses giving a mixture of nuclear recoils

Question 3

State two nuclei that are most likely to be used to form the plasma of a fusion reactor - method requires a plasma that has to be raised to a suitable temperature for fusion to take place

Answer 3

H-2

H-3

Question 4

State one method which can be used to raise the temperature of the plasma to a suitable temperature

Answer 4

Electrical heating

Question 5

Explain binding energy

Answer 5

Work must to be done separating nucleons from a nucleus in order to overcome the SNF. The potential energy of each nucleon is therefore increased when it is removed from the nucleus and so the energy needed to pull the nucleons apart is the same as the energy released when the nucleus is formed = the binding energy of the nucleus = work done/energy needed to separate a nucleus into its constituent nucleons = delta m * c^2

Question 6

Explain mass defect

Answer 6

for a reaction where no energy is supplied, the energy released, Q = delta m * c^2
Because the energy is released when a nucleus forms from separate protons and neutrons, the mass of a nucleus is less than the mass of the separated nucleons. is less than the mass of the separated nucleons. In any change where energy is released the total mass after the change is always less than the total mass before the change is always less than the total mass before the change because in the change, some of the mass is converted into energy which is released so as a nucleon joins together, the total mass decreases - this lost mass is converted into energy and releeased

Mass defect = mass of nucleus - mass of separated nucleons = (Z * mp) = ((A-Z) * mn) - mass of nucleus

Question 7

Binding energy (J) =

Answer 7

mass defect (kg) * c^2

Question 8

Binding energy (MeV) =

Answer 8

mass defect (u) * 931.5

Question 9

Annihilation –> 2 photons of energy =

Answer 9

E = mc^2 where m is the mass of the particles

Question 10

For a single gamma photon to produce a particle and antiparticle of mass m via pair production, its energy, E

Answer 10

> = 2mc^2

Not strict as extra energy is kinetic energy for the two particles.

Question 11

Average binding energy per nucleon =

Answer 11

average work done per nucleon to remove all the nucleons from a nucleus = binding energy/nucleon number

Question 12

Average binding energy per nucleon is a measure of… and is at a maximum at around

Answer 12

stability and is at a maximum at around A = 58, B.E = 8.7MeV where most stable nuclei occur (i.e. Iron where A=56)

Question 13

Average binding energy per nucleon can be used to estimate the… and is a useful way of…

Answer 13

energy released from nuclear reactions and is a useful way of comparing the binding energies of different nuclei

Question 14

Explain binding energy using the concept of mass defect

Answer 14

The mass of a nucleus is less than the mass of its constituent parts. The difference = mass defect. So as nucleons join together, the total mass decreases - this lost mass is converted into energy (E=mc^2) and released. If you pulled to nucleus apart, the energy you would have to use is = to the energy released when the nucleus is formed

Question 15

Combining small nuclei ____ the average binding energy per nucleon thus energy…

Answer 15

increases

is released

Question 16

Splitting large nuclei _____ the average binding energy per nucleon so energy….

Answer 16

increases

is released but < than fusion

Question 17

Combining large nuclei ____ the average binding energy per nucleon thus energy…

Answer 17

decreases

is required

Question 18

Splitting small nuclei _____ the average binding energy per nucleon so energy….

Answer 18

decreases

is required

Question 19

Making a nucleus from its parts ____ energy by…

Answer 19

gives out energy by losing mass therefore this energy = binding energy = energy needed to bind the nucleus together

Question 20

Iron is the most stable nucleus because…

Answer 20

it requires the most energy to break apart. The other elements need less to break apart

Question 21

The bigger the nucleus, the ____ energy…

Answer 21

the bigger the nucleus, the more energy you get out therefore bigger nuclei have larger mass defects

Question 22

Nuclei try to become stable like iron and so smaller nuclei ____ (and energy…) while larger nuclei _____ (and energy…)

Answer 22

Nuclei try to become stable like iron so smaller nuclei combine (and give out energy) to produce larger nuclei like iron via fusion while larger nuclei split up to produce smaller nuclei like iron (and give out energy) via nuclear fission)

Question 23

Nuclear fission is when

Answer 23

nuclei are split into two separate nuclei with smaller nucleon numbers meaning a difference average binding energy per nucleon

Question 24

Large nuclei fission

Answer 24

For large nuclei (A>56), energy increases as nucleons are lifted away from each other therefore mass increases so binding energy per nucleon increases when split into two smaller nuclei. Because binding energy is higher per nucleon (as the electrostatic repulsion is stronger but the SNF changes little, total energy change is greater therefore mass defect is greater and there is a bigger fall in potential energy meaning a decrease in mass equivalent to a release in energy to the surroundings.

Question 25

Small nuclei fission

Answer 25

For small nuclei (A<56), fission creates two new elements with lower binding energy per nucleon (higher up/less negative on the potential energy curve). Because binding energy per nucleon is lower (fewer neighbouring nucleons), total energy change is smaller so mass loss is smaller. Extra mass upon combination is equivalent to the gain in energy which is equivalent to the energy required from the surroundings.
As E=mc^2 = Binding energy per nucleon * nucleon number it requires energy to be put in to split the nucleus.

Question 26

Nuclear fusion =

Answer 26

is where two nuclei are combined to make one nucleus with a different average binding energy per nucleon and can release much larger amounts of energy compared to nuclear fission. The nuclear fusion of small nuclei occurs in stars.

Question 27

Fusion of small nuclei

Answer 27

For small nuclei (A<56), fusion increases the average binding energy per nucleon dramatically meaning that a lot of energy is released because they create a new element with more binding energy per nucleon and so mass decreases therefore energy decreases as released to surroundings

Question 28

Fusion of large nuclei

Answer 28

For large nuclei (A>56), form new element with less binding energy per nucleon therefore mass increases and so energy is required from the surroundings.

Question 29

Graph of average binding energy per nucleon, MeV (y axis) against nucleon number, A (x axis)

Answer 29

starts from just above origin and curves up to a peak then straight line ish down
r shape
Starts at H-2
Peaks at Iron (56, 8.7) - most stable
Uranium-235 is near end

Left of peak: energy released through fission
Right of peak: energy released through fusion

Question 30

Graph of potential energy per nucleon, MeV (y axis) against nucleon number, A (x axis)

Answer 30

Same as the binding energy curve but just reflected in the x-axis as potential energy is negative because work must be done separating the nucleons from the nucleus and so there is negative potential energy when the nucleons are together in the nucleus.