radioactivity review

four fundamental forces of nature

gravitational, weak nuclear, electrical magnetic, strong nuclear

what does strong nuclear force do

holds atomic nucleus together

holds nucleons in the nucleus , acts over a small distance

what is nuclear binding energy

energy required to split a nucleus into its components

higher binding energy =

a more stable nucleus and it takes more energy to pull the atom components apart

what is nuclear binding energy expressed in

MeV/ nucleon

to determine nuclear binding energy.. you must?

must determine the mass defect

what is the mass defect

difference between the mass of the nucleus and the sum of the mass of the nucleons

- actual mass of a nucleus is always less than the sum of its parts

what components do you need to calculate the mass defect

- actual mass of nucleus

- number of protons and neutrons

- masses of a proton and a neutron

average binding energy/nucleon of most nuclei

about 8 MeV

- lighter elements have less BE/ nucleon

what element has highest BE/ nucleon

Fe- 56

as nucleus becomes larger, BE/nucleon decreases slowly because why?

as nucleus gets bigger = the strong nuclear force only acts through small distances = so the force weakens/ nucleon decreases

fusion

when light nuclei combine

fission

when heavy nuclei break up

when does BE/nucleon increase and energy gets released?

when light nuclei combine, or heavy nuclei break up, or undergo radioactive decay

parent

unstable nuclei

daughter

more tightly bound than parent

what do unstable nuclei attempt to do?

attempt to maximize nuclear binding energy per nucleon via radioactive decay

chart of nuclides

- displays isotopes for each element

* not all isotopes are radioactive

as Z increases...

--> number of neutrons needed for stability increases

radioisotopes

- unstable because nucleus has too much energy

- decay to reach stable nuclear configuration

number of neutrons versus number of protons for isotopes determines type of decay process

can elements decay once stable?

no!

radioactivity

the emission of this excess energy (radiation) in an attempt to reach a stable state

by what processes does radioactivity occur

- electromagnetic radiation emission

* gamma rays

- particulate radiation emission

* alpha particle

* beta particle

half life (T 1/2)

the time required for a quantity of radioactive material to be reduced (decay) to half its original value

electromagnetic radiation - gamma decay

photons released from nuclei

electromagnetic radiation - x -rays

photons emitted from electrical orbital transitions are called x-rays

alpha decay

helium nucleus, slow and heavy 4 2 He

beta decay

electron (B- ) or position (B +)

ionization

- if this radiation is incident on some material, and the radiation has sufficient energy, it may ionize atoms in the material

- atom or molecule becomes an ion by addition or removal of an electron

how does decay happen?

decay results in conversion of mass to energy

- from mass difference between parent and daughter nuclei

- total mass- energy conversion amount

- most imparted as kinetic energy to the emitted particles or converted to photons

Q =?

transition energy

alpha decay formula

A number decreases by 4

Z number decreases by 2

beta minus decay formula

same mass number (A) but an increased atomic number (Z+1)

positron (beta plus) decay formula

Decreases the atomic number by 1 while keeping the mass number constant

alpha particle decay

happens in big nuclei

beta minus decay

neutron rich nuclei tend to decay this way

unhappy because there are too many neutrons

a neutron decays to a proton and a beta (-) particle, along with an antineutrino

- high speed electron ejected from the nucleus

- the ani-neutrino is essentially undetectable

- the anti- neutrino's main job is to carry excess energy away from nucleus

- the neutron is converted to a proton

positron (beta plus) decay

- neutron deficient nuclei undergo positron emission or electron capture

- a proton is converted into a neutron , a positron, and a neutrino = the positron and neutrino are ejected from the nucleus

- never occurs naturally = only found in nuclear experiments in reactors

- used in positron emission tomography (PET)

- wants more neutrons

B - beta particle

Bi is an electron but originates in nucleus

B + beta particle

B+ is considered antimatter

- travels through matter until encounters electron, annihilation event occurs

- two photons emitted in opposite directions (180 degrees)

- used in PET

electron capture formula

atomic number decreases by 1, mass number stays the same

electromagnetic decay - gamma ray emission formula

without changing its proton plus gamma symbol

electromagnetic decay - internal conversion

- energy transfer from nucleus to inner shell (K) electron (gamma ray is internally absorbed)

* conversion electron - discrete energies

internal conversion and gamma emission

they are competing mechanisms!

characteristic x ray

electrons cascade down to lower energy unoccupied shells , emitting x rays with well defined energies

auger electron emission

ejecting another outer shell electron after the inner shell vacancy is filled by an outer shell electron

AKA = change between K and L shell gives to M shell electorn

isomeric transition

for metastable nucleus

- excited states persists long time

decay diagram

used to illustrate decay modes of a radionuclide

- spacing = energy difference

- right arrow = Z increases

- left arrow = Z decreases

- vertical line in-between = no change in Z, or energy threshold AKA positron decay requires change in energy bigger than 1.02 MeV

decay constant

- radioisotope X (parent) ---> D (daughter)

- the number of atoms that disintegrate per unit time (CHANGE IN N/ CHANGE IN t) is proportional to the number of atoms (N)

how is radioactive decay a statistical phenomenon

one can not predict when a particular atom will decay

decay constant formula

Change in N/ Change in T) = - decay constant N = dN/dt = - y N

N = N sub 0 e ^ - decay constant t

exponential decay

quantity decreases at a rate proportional to its current value

activity formula

A = λN sub 0 e^ - λ t = A sub 0 e^ - λ t

SI units of activity

1 Bq

n = ?

n = t/T sub 1/2

number of half lives that have passed

after n half lives = (1/2)^n left

after 1 half life =

(1/2)^1 or 1/2 quantity left

after 2 half lives =

(1/2)^2 or 1/4 quantity left

after 3 half lives

(1/2)^3 or 1/8 quantity left

after n half lives =

(1/2)^n left

half life formula

A=A sub 0(1/2)^n or N = N sub 0 (1/2) ^n

secular equilibrium

quantity of radioactivity remains constant because its production rate (decay of parent) is equal to its decay rate

* T sub 1/2 of parent is very long compared to daughter

parent and daughter are in equilibrium

transient equilibrium

- daughter half-life is shorter than parent half life

- parent T sub 1/2 long but not infinite

- parallel decay rates - parent and daughter activites are decreasing but the ratio of activities is constant