E3 Radioactive decay

Radioactive

E3.1 Isotopes

Element = fixed nr of protons in atom

Diff nr of neutrons → isotopes

Know: hydrogen, deuterium, titrium (0,1,2 neutrons)

Z is constant, A is not.

Imbalance of prot/neutr → unstable → decay and emit radiation → stable

E3.2 Relative atomic mass

Average mass of element based on presence/abundance of different isotopes of element in a substance.

E3.3 Percentage abundance of isotope

How many of 100 atoms of this element are of this certain isotope → used to calc. relative atomic mass.

E3.4 Carbon Dating

Ratio of stable carbon-12 atoms to unstable carbon-14. Compare dead to living → see how many 14→12 (we know the rate so find the t)

Use half lifes

¹n + ¹⁴₇Nitrogen → ¹⁴₆Carbon + ¹p

E3.5 Radioactive decay

Spontaneous breaking of a nucleus to form more stable nucleus, resulting in emission of α, β or γ particle. Its random. can happen at any moment.

Spontaneous: not influenced by env. factors, random: time non-predictable

with lot of nuclei, possible to statistically predict using probs. for group

E3.6 Background Radiation

Ionising radiation present in environment, by natural/artificial sourceE

E3.7 Decay types

Imbalance of protons, neutrons, or energy → emit particles/radiation

alpha α

beta β

gamma γ

E3.8 Alpha decay

α : high energy He nucleus → 2prot, 2neutr → 4u mass, +2e charge

⁴₂α

emitted by large, unstable nuclei with too many nucleons (prot&neut)

Parent nucleus(^A_ZX)→ ⁴₂α + Daughter nucleus (^A-4_Z-2Y)

^A_ZX→ ⁴₂α + ^A-4_Z-2Y

E3.9 Beta-minus decay

β^- : high energy e^-, mass of 0.0005u and charge -1e

⁰_-1β^-

Too many neutrons: neutron turns into proton and emits electron + anti-neutrino → proton nr+1, nucleon nr constant

n → ⁰_-1β^- + v + p

^A_zX → ⁰_-1β^- + v + ^A_Z+1Y

the v is an antineutrino, we do later…

E3.10 Beta-plus decay

β⁺ : high energy positron: antimatter of electron: 0.0005u, +1e charge

⁰₊₁β⁺

Too many protons: proton turns into neutron and emits positron + neutrino → proton nr-1, nucleon nr constant

p → ⁰₊₁β⁺ + v + n

^A_zX → ⁰₊₁β⁺ + v + ^A_Z-1Y

E3.11 Gamma radiation

γ = high energy EM radiation = photon

Emitted by nuclei that need to lose some energy

⁰₀γ

proton and nucleon nr both constant.

^A_ZX → ⁰₀γ + ^A_ZY

E3.12 Ionising ability of α, β, γ

Measure of # of ionisation: when nuclear radiation pass through material

If radiation collides w. atom → it might knock out e^- : ionising atom.

Highly dangerous for living cells, α>β>γ

α: 3-5 cm traveled, highly ionising, weakly pen. , pass through paper

β: 20cm-3m, moderately, mod. penet, pass through alu foil

γ: infinite…, weakly ionizing, highly penetrating, pass through thick lead

E3.13 Penetrating power

distance nuclear radiation will travel before losing all its energy .

Shorter → shorter range in air. Highly ionising → pen. power

E3.14 Deflection in E and B-fields

In E field, β⁺ and α → - plate, β^- to + plate. γ non deflected

In B-field, also.

E3.15 Radioactive decay equations

1. too many n’s : β^- : ^A_zX → ⁰_-1β^- + v + ^A_Z+1Y

2. too many p’s: β⁺ : ^A_zX → ⁰₊₁β⁺ + v + ^A_Z-1Y

3. too many p/n’s: α. : ^A_ZX→ ⁴₂α + ^A-4_Z-2Y

4. too much E: γ; ^A_ZX → ⁰₀γ + ^A_ZY

E3.16 (anti-) neutrinos

Subatomic particles, no charge, no mass, also emitted…

antineutrino in β^- decay, neutrino in β⁺ decay. no relevance,except conserv E

Evidence: α have discrete E, β continuous, shared between β and v

E3.17 Activity + half life explained

Activity: nr of nuclei decaying in given time: Bq: 1 decay/s

Rate at which activity decreases is predictable:

Half life- time taken for half of nuclei to decay = half the activity aswell, constant, so t to go from 500→250 = t from 250 → 125.

Each isotope of each element has unique halflife, from 0.00001 s to 100000 years.

E3.18 Decay constant

λ : prob that individual nucleus decays per second; use average decay rate

Activity A = ^ΔN/_Δt = -λN (N=nr of undecayed nuclei in sample, ΔN = decayed)

Greater λ → greater A. - bc nr of nuclei remaining decreases over time.

N = N_oe^-λt

A = A_oe^-λt

C = C_oe^-λt (count rate…)

t_½ = ^{ln 2}/_λ

draw logN vs t_½ give linear graph with formula: ln N = -λt + ln N_o

Exponential decay: steeper slope: larger λ, N vs t, start at N_o

E3.19 Mass defect

Diff between measured mass of nucleus vs. sum of masses of constituents

Δm = Z(m_p) + (A-Z)(m_n) - m_{tot measur.}

We find that Δm = positive.

E3.20 Mass energy equivalence & binding energy

All masses have energy. Constituents of nucleus have larger m/E than final. Difference in energy: ΔE = Δmc², where m is the mass defect.

Binding energy: energy required to break nucleus into constituent p + n; making nuclei from system of pure p+n, releases E.

Can do binding energy per nucleon, or total.

ΔE = mc² is used in fission, fussion, weapons and particle collisions.

Careful with MeV, J, u etc…

E3.21 Binding energy per nucleon curve

More E/nucleon → more stable → more E to sep nucleons in this nucleus

first fusion: A+B→C, last: C→A+B. Iron most stable. : both release E

Greater mass defect → stabler.

E3.22 Strong nuclear force

1. Repulsive electric between + charges

2. Attractive grav bc of mass (neglible)

3. Strong nuclear force:attractive & stronger than electric repulsive

Acts between quarks (what prot/neut are made up of)

Strength depends on seperation between nucleons. Repulsive when too close, very attractive when mid, then slightly attractive. Very small range.

E3.23 Nuclear stability

Band of nuclear stabillity graph. First more stable when N=Z (up to z=20), then more neutrons than protons. Under line of stability;β⁺ decay, over: β^-. Top has mostly α.

E3.24 Nuclear Energy levels

Nucleus can exist in excited state similar to e^-. Once unstable nucleus decays: can emit gamma photons. Allowing the nucleus to lose energy. This happens after daughter nucleus is in excited state after decaying. Short excitation and moves to groun state quickly, via 1 or more steps.

Get weird graphs ???