Excelet

Mean Lifetime for Radioactive Decay

On statistical average, how long does a radioactive atom survive?

Let's explore mean lifetime for radioactive decay.

Please note that for both tabs you can rescale the time axis

Click on the tabs to navigate!!!

by changing the time-step at the bottom of the graph!

Mean Lifetime and Half-life 2000 cpt

rate or decay constant, k = 0.025 27.72 t 40 t

(average lifetime)

time, t Activity, A On statistical average, how long does a radioactive atom survive? decay

0.0 2000.0 equation

3.0 1855.5

6.0 1721.4

9.0 1597.0 half-life mean lifetime

12.0 1481.6 0 1000 0 735.7589

15.0 1374.6 27.72 1000 40 735.7589

18.0 1275.3 27.72 0 40 0

21.0 1183.1

24.0 1097.6

27.0 1018.3

30.0 944.7

33.0 876.5

36.0 813.1

39.0 754.4

42.0 699.9

45.0 649.3

48.0 602.4

51.0 558.9

54.0 518.5

57.0 481.0

60.0 446.3 time-step 3.00 (allows time scale to be adjusted)

initial activity, Ao =

t-1 half-life, t1/2 = mean lifetime, t =

A = Aoe -kt

Sinex 2015

0 10 20 30 40 50 60 700

500

1000

1500

2000

2500

735.758882342885

3

1000

3

2000.0f(x) = 2000 exp( − 0.025 x )

time, t

acti

vit

y,

A

The task:

Vary the rate or decay contant to see how

the mean lifetime responds.

How are the decay constant, half-live,

and mean lifetime related?

answer

2500 cpt

rate or decay constant, k = 0.0045 154 t 222.2222 t

(average lifetime)

time, t Activity, A decay

0.0 2500.0 equation

15.0 2336.8

30.0 2184.3

45.0 2041.7 initial rate line mean lifetime box

60.0 1908.4 0 2500 0 2500

75.0 1783.9 7.50 2415.625 222.2222 2500

90.0 1667.4 222.2222 0 222.2222 0

105.0 1558.6 the is the solid green line this the dashed orange line

120.0 1456.9 th diagonal in the orange box!!! plus the x and y axes

135.0 1361.8

150.0 1272.9

165.0 1189.8

180.0 1112.1

195.0 1039.6

210.0 971.7

225.0 908.3

240.0 849.0

255.0 793.6

270.0 741.8

285.0 693.4

300.0 648.1 time-step 15.00 (allows time scale to be adjusted)

Finding the initial number of nuclides, No initial activity, Ao =

t-1 half-life, t1/2 = mean lifetime, t =

A = Aoe -kt

Sinex 2015

0 50 100 150 200 250 300 3500

500

1000

1500

2000

2500

3000

3

2500.0f(x) = − 11.25 x + 2500f(x) = 2500 exp( − 0.0045 x )

time, t

acti

vit

y,

A

linear regression line

For more details, see:

The task of computations to find No:

Find the initial rate of decay at time, t = 0

= kAo

Find the x-intercept for the green

= y-intercept/(-slope) = Ao/initial rate

Find the area of the orange box, which is area under blue curve

= height * length = Ao t

Since Ao = kNo, find No = Ao/k

= Ao/k = No

McParland, Nuclear Medicine Radiation Dosimetry: Advanced Theoretical Principles, Springer, pp. 153-154 (2010).

Springer, pp. 153-154 (2010).