Decay Rate

Contents:•Probability of decay and Activity

•Whiteboard•Half life and exponential decay

•Whiteboard•Radiometric dating

N vs t

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TimeRe

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Probability and activity

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N - Number of un-decayed nuclei (number) - Per second probability of a nuclei decaying (s-1)A - Activity - decays/sec (Becquerels (Bq) = s-1)

A = -N/t = N

NA = 6.02 x 1023 atoms/moln = N/NA

n = (grams you have)/(molar mass)A = N 8.249 x 1016 s-1 = (2.098 x 10-6 s-1)N N = 3.93184 x 1022 nuclein = (3.93184 x 1022)/(6.02 x 1023 mol-1) = 0.065312954grams = n(molar mass) = (0.065312954)(222.02) = 14.5 g

Example - Radon 222 has an atomic mass of 222.02. How many grams of it do you have if your activity is 8.249 x 1016 decays/sec, and your decay probability is 2.098 x 10-6 s-1? (4)

Whiteboards: Activity and decay probability

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W

A = N = (3.19 x 10-10 s-1)(5.12 x 1023) = 1.63 x 1014 decays/s (or s-1)

What is the activity if you have a of 3.19 x 10-10 s-1, and you have 5.12 x 1023 un-decayed nuclei?

1.63 x 1014 decays/sec

W

A = N 1420 s-1 = (1.27 x 1020) = 1.12 x 10-17 s-1

What is the if 1.27 x 1020 un-decayed nuclei generate 1420 decays per second?

1.12 x 10-17 s-1

Half life and exponential decay

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- Per second probability of a nuclei decaying (s-1)N - Number of un-decayed nuclei (number)A = Activity - decays/sec (s-1)A = -N/t N = Noe-t - Exponential decay

No - Original valueN - Value at time tt - Elapsed time

Diff EQ…

A = N = Noe-t

Half life

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T1/2 - Half life - time for half nuclei to decay1/2No= Noe-T1/2

1/2= e-T1/2

2 = eT1/2

ln(2) = T1/2

T1/2 = ln(2)/

Half life and exponential decay

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A = N = Noe-t A = -N/tN = Noe-t

T1/2 = ln(2)/N vs t

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Time

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Half lives occur over and over

Half life here is 20 s

Half life and exponential decay

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Example: Bi 211 has a half life of 128.4 s. What is the per-second probability of a nuclei decaying? If you start out with 32 grams of Bi 211, how much is left after 385.2 s? After what time is there 23 grams left? What is the activity when there is 23 grams left? (m = 210.987 u)Use formulasCheat (385.2 s = 3 half lives)

A = N = Noe-t A = -N/tN = Noe-t

T1/2 = ln(2)/

Example: Bi 211 has a half life of 128.4 s. What is the per-second probability of a nuclei decaying? If you start out with 32 grams of Bi 211, how much is left after 385.2 s? After what time is there 23 grams left? What is the activity when there is 23 grams left? (m = 210.987 u)

so the = ln2/128.4 = 0.005398343 s-1.and the N (just use grams) at 385.2 seconds would be:N = Noe-t = (32 g)e-(0.005398343 s-1)(385.2 s) = 4.0 g(How come it is exact??? – 385.2 = 3*128.4 so it is exactly 3 half lives. look for that on tests and stuff.)

Use the same formula for finding the time it will be 23 g (less than one half life 128.4 s – right?)N = Noe-t(23 g) = (32 g)e-(0.005398343 s-1)t

so t = 61 s

Activity is just given by A = N, so we use chemistry to find N:N = (6.02x1023atoms/mol)(23 g)/210.987 g/mol) = 6.56249E+22 atomsso A = N = (0.005398343 s-1)(6.56249E+22 atoms) = 3.54266E+20 counts per second

Whiteboards: Half Life and Decay

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W

T1/2 = ln(2)/= ln(2)/(8.91 x 10-8 s-1) = 7779429.636 s = 90.0 days

Oregonium has a decay probability of 8.91 x 10-8 s-1. What is its half life in days?

90.0 days

T1/2 = ln(2)/- (in data packet)T1/2 = (96.23 min)(60 sec/min) = 5773.8 s

= ln(2)/ = ln(2)/(5773.8 s) = 0.0001201 s-1

What is the nuclear decay probability of a substance that has a half life of 96.23 minutes?

0.0001201 s-1 W

N = Noe-t - (in data packet)N = (1250) e-(8.91x 10-8)(30*24*3600)

N = 992 g

Oregonium has a decay probability of 8.91 x 10-8 s-1. If you have 1250 grams of Oregonium initially, how many grams do you have after 30.00 days? (x24x3600)

992 g W

60 seconds is exactly 5 half lives, so divide in half five times64/25 = 2.0 grams

Tualatonium has a half life of 12 seconds. If you start with 64 grams of it, how much remains after a minute? (Cheat)

2.0 grams W

= ln(2)/T1/2 = 0.083111173 s-1

N = Noe-t - (in data packet)N/No = e-t

ln(N/No) = -tln(No/N) = tln(No/N)/ = t = ln(1350/125)/(0.083111173 s-1)t = 28.6 s

Tigardium has a half life of 8.34 seconds. The initial activity is 1350 counts/second, after what time is the activity 125 counts/sec?

28.6 s W

N = Noe-t - (in data packet)N/No = e-t

ln(N/No) = -tln(No/N) = tln(No/N)/t = = ln(1245/938)/(180. s) = .001573 s-1

T1/2 = ln(2)/(.001573 s-1) = 441 s

A certain substance has an activity of 1245 counts/sec initially, and an activity of 938 counts/second after exactly 3.00 minutes. What is the half life of the substance?

441 s W

Radiometric dating

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Know original proportion of unstable nucleiMeasure current proportionUse N = Noe-t to calculate elapsed timeCarbon 14 dating:

C14 created in atmosphere (T1/2 = 5730 Y)Living things absorb C14 in known amountsThey die, and quit absorbing C14

Rocks can be dated Hardening forms nearly pure crystalsMagma is product of fission within the earthLead - Earth’s age - Uranium/Lead - Clean room - lead in fuel.