Physics 1102 In-Class Problems: Radioactivity

1. The alpha-decay of ²³⁸U releases 4.25 MeV of energy. Virtually all this energy is in the form of the kinetic energy of the alpha-particle. How fast is the alpha particle travelling?
   

2. A neutron outside the nucleus decays into a proton, an electron, and a neutrino. Note that n = 1.008665 u, p = 1.00728 u, and e = 5.48578 × 10^-4 u. Assume that the neutrino is massless.
   (a) Assuming the neutrino is massless, how much energy is released?
   (b) Assuming that all this energy is converted into the kinetic energy of the electron, how fast is the electron moving?
   

3. Consider ³¹P which has 15 protons and 16 neutrons. Find the binding energy per nucleon. Note that n = 1.008665 u, ¹H = 1.007825 u, and ³¹P = 30.973762 u.
   

4. Graph the data below and determine the decay constant and the half-life using LineFit.
   

   Time t min	Counting Rate R Counts/min
   60	3100 ± 110
   120	2400 ± 100
   240	1500 ± 80
   360	985 ± 60
   480	525 ± 50
   600	310 ± 40
   720	220 ± 30

5. A Geiger counter, held 15.0 cm away from a small piece of radioactive ore, records a constant 192 counts per second. The Geiger counter is only recording the number of radioactive particle through the end of the counter. The end of the counter has an area of 2.00 cm².
   (a) What is the total activity of the ore sample?
   (b) Chemical analysis indicates that there is 6.256 × 10²¹ radioactive nuclei present in the sample. What is the decay constant and half-life?
   

6. In a sample of wood found at an archeological dig, the ratio ¹⁴C to ¹²C is found to be only 23.4 ± 0.2% of that found in living organism. The half-life of ¹⁴C is 5370 years. Determine how long ago the tree died.

Questions? mike.coombes@kwantlen.ca