Suppose a radioactive nucleus has a half-life of 2 min. and suppose the counting
ID: 1575640 • Letter: S
Question
Suppose a radioactive nucleus has a half-life of 2 min. and suppose the counting rate at t = 0 is 3000 counts/s.
a. What is the counting rate after 2 min?
b. After 6 min?
c. After 10 min?
d. After 20 min?
e. 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?
Explanation / Answer
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
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