Question

(a) The ²¹⁰Po source used in a physics laboratory is labeled as having an activity of 1.00 µCi on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1000 counts per minute. She notices that the source was prepared 106 days before her lab. What fraction of the decays is she observing with her apparatus?
%

(b) Identify some of the reasons that only a fraction of the αs emitted are observed by the detector.

Answer 1

T = half life of 210Po = 138.4 days

t = time before source was prepared = 106 days

using the formula

= decay constant = 0.693 /T = 0.693/138.4

t = (0.693/138.4) (106) = 0.531

A_o = initial activity = 1 x 10^-6 Ci = 1 x 10^-6 x 3.7 x 10¹⁰ disintegration/s      since 1 ci = 3.7 x 10¹⁰ disintegration/s

A_g = given activity = 1000 counts/min = 1000/60 disintegration/s = 16.7 disintegration/s

using the formula

A = activity after 106 days = A_o e^-t

A = (1 x 10^-6 x 3.7 x 10¹⁰) e^-0.531

A = 2.18 x 10⁴

ratio = A_g/A = 16.7 / (2.18 x 10⁴) = 7.7 x 10^-4