Intro Nuclear Engineering Quiz 1

how long does it take to build a reactor?

10 years

What is the biggest expense of a nuclear reactor?

interest on the the high capital expenditure, fuel costs are low

fast neutrons

high energy, >1 MeV, produced by fission

thermal neutrons

lower energy, <0.025 eV, likely to cause further fission

what is a nuclear moderator used for?

slows down fast neutrons so they can sustain a nuclear chain reaction

fissile elements

undergo fission if they capture an extra neutron

fertile isotopes

don’t undergo fission, can capture a neutron to turn into a fissile isotope

fission process

1. slow neutron approaches fissile nucleus

2. strong interaction leads to capture

3. unstable nucleus oscillates, increased sfc energy, decrease BE between nucleons

4. unstable nucleus decays

5. 2 fission products form (usually different mass) and 2-3 neutrons

Becquerel (Bq)

number of nucleus decays/second

Radioactivity or Activity formula

A = m/ma*N*lambda, m = mass of isotope, ma = atomic mass, lambda = decay const., N = avogadro’s const.

absorbed dose (D)

energy deposited by radiation in a material

absorbed dose formula

D = d(epsilon)/dm, d(epsilon) = mean amount of energy, dm = unit mass

Gray (Gy)

unit of absorbed dose, J/kg

Equivalent dose (HT)

Absorbed dose with weighting factor to account for type of radiation

x-ray, gamma ray, electron weighting factor

1

alpha, heavy ion, fission products weighting factor

20

Equivalent Dose Formula

HT = sum(WR*DT,R), WR=weighting factor for type of radiation, DT,R = absorbed dose

Effective dose (E)

equivalent dose with weighting factor to account for radio-sensitivity of tissues

Effective dose formula

E = sum(WT*HT), WT = weighting factor for type of tissue, HT = equivalent dose

Sievert (Sv)

unit of equivalent and effective dose, J/kg

Stochastic radiation effects

probability of an effect occuring is a function of dose, no threshold dose, cancer

Non-stochastic radiation effects

severity of effect is a function of dose, threshold dose, skin damage

Aim of radiation protection

reduce probability of stochastic, prevent non-stochastic effects

Radiation Carcinogenesis Model

probability of cancer is linearly proportional to radiation dose

T or F: any radiation dose, no matter how small can cause cancer.

T

0-0.25 Sv effect

no detectable effect

0.25 - 1 Sv effect

short term reduction of some blood cells, no long term effect

1 - 2 Sv

nausea, fatigue, possible vomiting, long-term blood cell damage

2 - 3 Sv

nausea, vomiting day 1, radiation sickness after 2 weeks, 3 month recovery

3 - 6 Sv

nausea, vomiting, diarrhea after a few hours, intense radiation sickness after 1 week, death possible after 2-6 weeks

>4.5 Sv

50% chance of death

>6 Sv

death nearly 100% likely

Intensity of radiation formula

I = I0*exp(-n*sigma*x) = I0*exp(-mu*x), n = number of atoms/cm³, mu = linear attenuation coeff, sigma = absorption cross section, x = thickness of material, I0 = initial intensity

linear attenuation coeff

fraction of radiation beam that is absorbed or scattered per unit thickness of the material, aka absorption coeff, depends on radiation energy, cm^-1

mass attenuation coeff=

mu/rho, (cm²/g) mu = linear attenuation coeff, rho = density

mass thickness=

rho*x, rho = density, x = thickness of material

absorption cross section

material constant dependent on PROBABILITY of the particle being scattered or absorbed, cm²

attenuation length/mean free path

1/mu, reciprocal of linear attenuation coeff, average distance travelled by a particle before being absorbed or scattered

half-value layer (HVL)

thickness of material required to reduce intensity of radiation by 50%

HVL=

0.693/mu

Fundamental protective measures to reduce external exposure to radiation

MINIMIZE time, MAXIMIZE distance, use SHIELDING

total irradiation does not degrade properties of material to any significant extent over time

material used as shielding

total irradiation changes material properties

radiation damage/effects

Photoelectric effect

gamma photon ejects electrons through transfer of energy

ejected electron kinetic energy formula

KE = E(gamma) - BE, E(gamma) = photon energy, BE = electron binding energy

Photoelectric effect dominant for

<200keV

X-ray emission

released when electrons drop to lower energy orbitals

Compton Scattering

gamma photon ejects electron, but still has enough energy to keep scattering as a lower-energy photon

Compton Scattering dominant for

100 keV - 10MeV

compton edge

maximum possible energy of ejected compton electron

Compton edge formula

E = E(gamma)/(1+4*E(gamma))

Compton scattering formula

wavelength - wavelength’ = h/(me*c)*(1-cos(theta)), wavelength = of incident photon, wavelength’ = wavelength of scattered photon, h = plancks const, me = electron rest mass, c = speed of light, theta = scattering angle

pair production

incident photon interacts with nucleus via COULOMB force and converts into electron-positron pair

positron after pair production

combines with electron and produces two gamma photons

pair production dominates for

1 - 10 MeV

in order of decreasing gamma photon energy types of ionization

pair production, compton scattering, photoelectric effect

Photoelectric effect absorption cross section formula

sigma(pe) = (Zeff)^5/(Ei)³, Ei = incident photon energy

Zeff =

sum(xi*Zi), Zi = atomic number, xi = weight % in the material

Compton scattering absorption cross section formula

sigma(c) = Zeff/Ei, Ei = incident photon energy

Pair production absorption cross section formula

sigma(pp) = (Zeff)²*ln(2*Ei), Ei = incident photon energy

total absorption cross-section formula

sigma(T) = sigma(pe) + sigma(c) + sigma(pp)

Energetic particles ____ atoms as they move through solids, liquids, or gases

ionize

stopping power

average energy loss per unit path length, MeV/cm

electronic stopping

slowing down via inelastic collisions between electrons and ion

nuclear stopping

slowing down via elastic collisions between radiation particle and atoms

Stopping power formula

S(E) = Se(E) + Sn(E), Se = electric stopping, Sn = nuclear stopping

Bragg peak

radiation particle’s ionization density increases as it slows down, until it is completely out of energy

range of alpha particle in medium other than air formula

Rm = Ra*(rho(a)/rho(m))*(Am/Aa)^(1/2), m = medium, a = air, rho = density, R = range, A = atomic weight

Linear Energy transfer (LET)

amount of energy ionizing particle transfers to medium it’s passing through, similar to stopping power except doesn’t include nuclear stopping, keV/micrometer

Linear energy transfer formula

L = dE/dx, E = energy, x = distance

Radiation damage process

1. transfer of energy from incident radiation to lattice atom, causes PKA

2. movement of PKA away from lattice site, causing other displaced atoms

3. displacement cascade, vacancies and interstitials cluster

4. some recovery

point defects

vacancies, interstitials

electronic defect

missing/trapped electrons, excited states

bubbles defect

gas atoms occupying voids

dislocations defect

line defects at grain boundaries

loop defect

line defects that loop back on themselves

frenkel pair defect

atom displaced causes vacancy and interstitial

Schottky defect

equal number of cations and anions missing, creating vacancies but maintaining charge balance

high temperature dominant defect

void swelling

low temperature dominant defects

atoms cannot move as easily, so defects cannot annihilate, material becomes amorphous

amorphous material

lost its crystalline structure

criteria for radiation tolerance

resistance to void swelling and amorphization

critical amorphization dose

at given temperature, dose at which material amorphizes

critical amorphization temperature

at given dose, temperature at which it is no longer possible to amorphize

displacement cross section

probability lattice atom will be displaced by flux of particles

total damage to material

displacements per atom, dpa or displacements per atom over area, dpa/cm²

Ed

threshold displacement energy

E1

cut off energy

T

pka kinetic energy

0 < T < Ed, v(T)?

0

Ed < T < 2Ed, v(T)?

1

2Ed < T < E1, v(T)?

T/2Ed

E1 < T < inf, v(T)?

E1/2Ed

Kinchin-pease model

estimation of atoms displaced by PKA

above E1

recoils lose energy through electron excitation

below E1

recoils lose energy through hard-core elastic scattering

gaseous diffusion

UF6 gas passed through porous membranes, lighter U235 diffuses faster than heavier U238, energy intensive

gas centrifugation

UF6 is spun, heavier U238 move to outside and lighter U235 stays near the center, 10x more efficient than diffusion

UF6 production

U308 ore is milled, then reduced to UO2, converted to UF4, oxidation to UF6

Breeding Ratio (R)

average number of fissile atoms produced per fission event, measure of reactor performance