Question

The 210Po source used in a physics laboratory is labeled as having an activity of 1.0μCi on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the source was prepared 120 days before her lab. What fraction of the decays is she observing with her apparatus?

a) 1/8
b) 1/4
c) 1/2
d) 3/4

Answer 1

The fraction of the decays observed by the student is 1/8. Therefore, the fraction of the decays observed by the student is 1/8 option a.

Step-by-step explanation:

The fraction of the decays that the student is observing with her Geiger counter can be determined using the concept of activity and the equation for radioactive decay. The activity of a radioactive substance is proportional to the number of decays per unit time. The equation for activity is given by:

Where N is the number of radioactive nuclei and t1/2 is the half-life of the substance.

In this case, the activity of the 210Po source is 1.0 μCi (microcurie) and the student observes 1500 counts per minute with her Geiger counter. To find the fraction of decays observed, we need to compare the observed activity with the initial activity. Using the equation for activity, we can set up the following proportion:

Observed activity / Initial activity = Observed decays / Initial decays

Let x be the fraction of decays observed. The observed activity is 1500 counts per minute and the initial activity is 1.0 μCi. The initial decays can be calculated using the equation for activity:

Initial decays = Initial activity / (0.693 × t1/2)

Substituting the given values, we have:

1500 / 1.0 × 10-6 Ci = x / (1.0 × 10-6 Ci / (0.693 × t1/2))

After simplifying the equation, we get:

x = 1/8

Therefore, the fraction of the decays observed by the student is 1/8 option a.