Pre-Lab 13 Assignment: Radioactive Decay

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Name: Lab Partners: Date: Lab 13: Radioactive Decay Objectives • To understand phenomena that have an exponential behavior. • To determine the relationship between the decay constant and the half-life. • To determine the half-life of an unknown radioactive sample. Overview In Lab 7 (Capacitors and RC Circuits) we learned that when a resistor and a capacitor are connected to a battery and a switch the capacitor will charge and discharge following an exponential behavior. During the charging process the voltage in the capacitor is given by the following equation: V = V 0 (1−e −t/τ ), (1) where τ = RC, and R is the resistance of the resistor and C is the capacitance of the capacitor. The discharge is given by V = V 0 e −t/τ . (2) The constant τ called the characteristic time (or ”time constant”) tells how fast or slowly the capacitor will be charged. The larger the value of τ the more time it will take to charge the capacitor and this will depend on the values of R and C. The constant τ also tells how fast or slowly the capacitor will be discharged. For example, from Eq. (2), at time t = τ, V = V 0 e −τ/τ = V 0 e −1 = 0.37V 0 ; that is, after τ seconds, the voltage is reduced to 37% of the original value. Question 0.1 In the axes below an exponential decay of an RC circuit with a 100Ω resistor and a capacitor of unknown capacitance is shown. Determine the time constant τ for the circuit. Show all your work. PHYS-204:Physics II Laboratory 1
Radioactive Decay v 0.1 10 9 8 7 6 Voltage (V) 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Time (s) Question 0.2 Using the result from Question 0.1 determine the capacitance of the capacitor. show your work Question 0.3 Using the graph above determine at what time the voltage dropped to about 5% of its original value. This value corresponds to approximately how many time constants (τ)? Many other phenomena have exponential behavior such as population growth and decay and radioactive decay. In this lab we will examine the exponential decay of a radioactive sample with a short characteristic time. Radioactivity is a result of the disintegration or decay of unstable nuclei. Because of this instability the nucleus will decay with the emission of some kind of radiation which can be a particle or electromagnetic radiation. The rate of decay of a PHYS-204:Physics II Laboratory 2
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Pre-Lab 13 Assignment: Radioactive Decay

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