Question

R= Ro(1/2)n n= number of half lifetimes= t/t1/2 (a)n= 2/2= 1 R= Ro(1/2)n R=3000(1/2)1 R= 1500 counts/sec (b)n= 6/2= 3 R= Ro(1/2)n R=3000(1/2)3 R= 375 counts/sec (c) n= 10/2= 5 R= Ro(1/2)n R=3000(1/2)5 R= 93.75 counts/sec (d) n= 20/2= 10 R= Ro(1/2)n R=3000(1/2)10 R= 2.93 counts/sec

What is the mean life of this nucleus?

f. Suppose that the Geiger counter detects 10% of all the radioactive decays.

What is the total number of radioactive nuclei at time t = 0?

g. What is the total number at t = 2 min? h. How many nuclei decay in the first 2 minutes?

i. What is the initial decay rate?

j. Why is the answer in h. not equal to the answer in i. times 120 sec?

Answer 1

During half life (t_1/2)the count of nucleus reduces to the half of the previous value.

The answer for Question e:

The mean life of a radioactive nucleus is given by:

From the given information (a-d),

Thus

The answer for Question f:

Let the actual count be x. The counts detected by Geiger counter is only 10% of x which is:

10% x = 3000 counts

Thus, x = 3000/0.1 = 30000 nuclei

The answer for Question g:

From Question f, the initial counts were 30000 nuclei

Thus at t = 2 min = t_1/2, only half of the nuclei will remain which is 15000 nuclei.

The answer for Question h:

Since half of the initial nuclei (30000 nuclei) remains after first two minutes, the deayed nuclei were given by:

Nuclei decayed after first 2 min = Initial nuclei - nuclei remained after 2 mins = 30000 - 15000 = 15000 nuclei

The answer for Question i:

The initial decay rate is given by,

where x is the initial nuclei count (30000)

Thus,

The answer for Question j:

The answer for h is the number of nuclei decayed at t = 2 min while the answer for i is the initial decay rate. Since the decay rate changes over the period of time, both of them will never be the same.