Radioactive Decay The nuclei of some chemical elements are unstable against the strong nuclear force holding them together, resulting in a spontaneous.

Radioactive Decay

• The nuclei of some chemical elements are unstable against the strong nuclear force holding them together, resulting in a spontaneous change of characteristic or identity of the element.

• This is especially common for elements above 92

• There are 3 methods of decay

Decay Mechanisims

- decay

- decay

- decay

• A Helium nucleus seems to emerge from the unstable element

• An electron and neutrino emerge from the unstable element

• A photon emerges from the unstable element

- decay

• Helium nucleus emerges from the unstable element.

• 92 238U 90

234Th + 24He + energy

• electric repulsion becomes greater than the nuclear attraction/ contrast between short and long range forces.

• Masses do not balance! …Why?

- decay

• An electron and a “neutrino” emerge from the unstable nucleus.

• 614C 7

14N + - 10e + energy

• Weak force - a “down quark” in a neutron changes into an “up quark” changing it into a proton.

• Masses do not balance! …Why?

- decay

• Photon emerges from the unstable element

• The element retains its identity

• 13 27 Al* 13 27 Al + + energy

• nucleus is not changed but has an excess of energy - particles are agitated and farther away from each other.

• Masses don’t balance!

Masses don’t balance!

• Einstein - mass IS energy

• E = mc2

m is the mass difference between the parent nuclei and the daughters. The equation gives the energy released. Mass is converted into energy!

Decay Process

• The fraction of atoms decaying in a time

interval t is:

– The value of depends on the nucleus

– The unit of is 1/seconds (per second)

N / N = - t

Decay Measurement In the LabMeasuring λ for an element: Villanovium

N / N = - t

1. How may atoms of Villanovium?

3. Count decay particlesduring time interval

2. Timer forGeiger Counter

Vu

The Decay Equation

• The fraction of atoms decaying in a time interval t is:

• Using calculus on this equation, we get:

N(t) - # at time t N0 - # at beginning

t - elapsed timee = 2.71828…

N / N = - t

N(t) / N0 = e -t

Decay Equation – how it works

• How does N(t) decrease with time? N(t) / N0 = e -t

Fraction decaying each second - λ 0.110 %

tAmount at time, t

tAmount at time, t

0 1.0000 0 1.00001 0.9000 1 0.90002 0.8100 2 0.80003 0.7290 3 0.70004 0.6561 4 0.60005 0.5905 5 0.50006 0.5314 6 0.40007 0.4783 7 0.30008 0.4305 8 0.20009 0.3874 9 0.100010 0.3487 10 0.000011 0.3138 11 -0.100012 0.2824 12 -0.200013 0.2542

ADD a fraction each time – compound interest

N(t) / N0 = e +t

Fraction increasing each year, + λ 0.055% INCREASE each time 5 %

tAmount at time, t

tAmount at time, t

0 1.0000 0 1.00001 1.0500 1 1.05002 1.1025 2 1.10003 1.1576 3 1.15004 1.2155 4 1.20005 1.2763 5 1.25006 1.3401 6 1.30007 1.4071 7 1.35008 1.4775 8 1.40009 1.5513 9 1.450010 1.6289 10 1.500011 1.7103 11 1.550012 1.7959 12 1.600013 1.8856

Decay Equation – how it works

• Suppose 10% decays each second: N(t) / N0 = e -t

Fraction decaying each second - λ 0.110 %

tAmount at time, t

tAmount at time, t

0 1.0000 0 1.00001 0.9000 1 0.90002 0.8100 2 0.80003 0.7290 3 0.70004 0.6561 4 0.60005 0.5905 5 0.50006 0.5314 6 0.40007 0.4783 7 0.30008 0.4305 8 0.20009 0.3874 9 0.100010 0.3487 10 0.000011 0.3138 11 -0.100012 0.2824 12 -0.200013 0.2542

50%, half-life

Half-Life – when ½ remains

• Half-life [ t½ ] when 10% decays in a second --- about 6.4 seconds

N(t) / N0 = e -t

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

NEVER REACHES 0

Seconds

If you know , you can find t1/2

• Suppose that 50% is left, then:

• Since we know we can solve for “t1/2”. We call that time the half-life – how long it takes (in seconds) for ½ of the sample to decay.

N(t) / N0 = e -t = 0.5

Half-life examples

Isotope Half-LifeCesium 137 30 YearsChromium 51

27.7 DaysCobalt 57 271.7 DaysCobalt 60 5.26 YearsCopper 64 12.7 HoursFluorine 18 109.7 MinGadolinium 153

242 DaysGallium 67 3.26 DaysGold 198 2.7 DaysIndium 111 2.81 DaysIodine 123 13.2 HoursIodine 125 59.6 DaysIodine 131 8.02 Days

Isotope Half-LifeIridium 192 73.83 DaysMolybdenum 99

66 HoursPhosphorus 32

14.29 DaysSamarium 153

46.7 HoursSelenium 75

119.8 DaysStrontium 89

50.5 DaysTechnetium 99m

6.01 HoursThallium 201

3.04 DaysXenon 133 5.2 DaysYttrium 90 64 Hours