Question

1. Suppose that you are given a 200 gram sample of a radioactive substance with a half-life of 45 days. How many grams will be left after 360 days?

2. A radioactive substance is found to register 5000 counts per second on a Geiger counter. Twenty-four hours later it registers 1250 counts per second. What is its half-life?

3. If a sample emits 2000 counts per second when the detector is 1 meter from the sample, how many counts per second would be observed when the detector is 3 meters from the sample?

4. Using the sample in question 3, how many counts per second would be observed when the detector is 10 meters away from the sample?

5. If a 10 gram sample of a radioactive substance has a half-life of 6000 years, how much would be present after 8000 years?

6. If Nitrogen-14 absorbs an alpha particle and then emits a Hydrogen-1, what is the resulting nucleus?

7. If Au-185 emits an alpha particle, what is the nucleus formed?

8. What nucleus emits an alpha particle and forms Th-234?

9. If Th-234 emits a beta particle, what nucleus is formed?

10. If Nitrogen-14 absorbs a neutron and then emits a Hydrogen-1, what nucleus is formed?

Answer 1

1) let lamda is the decay constant.

lamda = 0.693/(T1/2)

= 0.693/45

= 0.0154 day^-1

mass of the substance remaining after t days,

M = Mo*e^(-lamda*t)

= 200*e^(-0.0154*360)

= 0.782 grams

2) let lamda is the decay constant.

use,

A = Ao*e^(-lamda*t)

A/Ao = e^(-lamda*t)

lamda = -ln(A/Ao)/t

= -ln(1250/5000)/24

= 0.05776 hour^-1

half life time, T1/2 = 0.693/lamda

= 0.693/0.05776

= 12 hours

3) when the detector is 3 meters from the sample the no of counts obsrved,

N = 2000*(1/3)^2

= 222 counts per second

4) when the detector is 10 meters from the sample the no of counts obsrved,

N = 2000*(1/10)^2

= 20 counts per second