Nuclear Radiation

Name	Definition	Formulae
NUCLEAR DECAY
Nuclear decay	Randomly: It is unpredictable which nucleus will decay next and when it decays Spontaneous: the rate of decay cannot be changed by changing the external conditions (temperature, pressure, etc.)
Radioactive isotopes	Isotope has an unstable nucleus, decay and emit radiation
Alpha decay	Alpha particles: Strongly ionizing Short range in air Stopped by paper Deflected by magnetic fields	$_{92}^{238}textrm{U}rightarrow _{90}^{234}textrm{Th}+_{2}^{4}textrm{a}$ Alpha decay ↓ Z by 2, A by 4
Beta decay	Beta particles are high-speed electron emitted by the nucleus Beta particles Moderately ionizing Range in air bout 1m Stopped by thin metal Deflected by magnetic fields (opposite direction to alpha)	$_{6}^{14}textrm{C}rightarrow _{7}^{14}textrm{N}+_{-1}^{0}beta+v_{e}^{-}$ Beta decay ↑ Z by 1 v: neutrino ve : electron neutrino $v^{-}e$ : anti-electron neutrino
Gamma decay	Gamma rays are high energy EM radiation (photon) Gamma rays: Weakly ionizing Obey inverse square law in air Stopped by 1m concrete Not deflected by magnetic fields
HALF-LIFE
Half-life	The time is taken for the number of radioactive nuclei to reduce into half of its initial value	$N=N_{o}e^{-lambda t}$
Decay constant	The probability that a given nucleus will decay in one second	$lambda =frac{ln2}{T1/2}$
Activity	The rate of decay of unstable nuclei Unit: Bq (Becquerel)	$A=A_{o}e^{-lambda t}$
Rate of production	The rate of production of C-14 (etc.) decrease The ratio was greater Ratio used is from current time not from the past So, the time is underestimated
BACKGROUND RADIATION
Background radiation	Radioactive isotopes in the environment Sources of radiation: rocks, air, water, cosmic rays Background radiation may affect cancer rate, responsible for some mutations that drive evolution	Before plotting activity graph the count rate must be corrected for background, otherwise 1/2 will be overestimated

Name	Definition	Formulae
BINDING ENERGY
Mass defect	Free nucleons have more energy than when they’re trapped in the nucleus. According to Einstein, $E=mc^{2}$ so if the energy of the nucleus increases the mass must increase Since the mass of proton/neutron is constant, the mass of the nucleus < total mass of proton/neutron in it.	= Mass of necleons -Mass of nucleus
Nuclear binding energy	The energy needed to separate all nucleons in the nucleus	$B.E.=Delta mc^{2}$
	56 is the most stable isotope For A>56 the BE/nu decrease So required net energy input to undergo fusion So does not occur in massive stars
FISSION
Nuclear fission	Split a large nucleus into small nuclei Release energy because the BE/nucleons of the fragment increase→ the energy is released in the reaction, provided that we do not pass the peak Number of neutrons always increase
Chain reaction	More than 1 neutron is produced in the reaction. Each neutron can induce further nuclei to fission The reaction grows exponentially
Fissile	Nucleus can be split by slow neutron
Rate of energy radiation
Rate of temperature	Most KE released is carried by the alpha particles which escapes, so it does not heat the metal.	$frac{dQ}{dt}=mcfrac{dT}{dt}$
increase	So, rate of T is likely to be overestimated
Radioactive waste	Total activity is underestimated All isotopes produced in the decay will be radioactive, so they contribute to the total
FUSION
Nuclear reactor	Pros: Lots of energy/kg of fuel No CO2 emission Cons: Radioactive waste must be stored for thousands of years Possibility of radiation escape during accident High cost of building reactors and decommissioning
Nuclear fusion	Joining 2 or more light nuclei into a heavier one and release energy
Sustained fusion	High energy/ temperature →The particles have enough kinetic energy to overcome electrostatic repulsion →They come close enough for fusion High density/ pressure → Ensure that the reaction rate is high
Fusion reactors	Pros: Unlimited supply of fuel Little radioactive waste Cons: Very expensive, requires extremely high T, P → Container problems Strong magnetic field required