The neutrons emitted by the source lose energy in the water. To activate the sample, the Vanadium foil is placed in a water tank close to the neutron source (several centimeters away). This experiment therefore requires a nuclide with a short enough half-life to provide enough decay data in the relatively short duration of this teaching class.Ī popular method of producing short-lived activity is to activate a natural metal (such as Vanadium) with a neutron source such as 252Cf or an Americium/Beryllium combined source. Equation 5-9 demonstrates that this is inversely proportional to the half-life. The figure shows the exponential nature of the radioactive decay.įigure 5-1: The observed counts of 52V with background subtraction as a function of time.Įquation 5-1 shows that the amount of decay (or emitted radiation) is proportional to the decay constant. The figure below shows an example of 52V decay by measuring the counts observed as a function of time (following a subtraction of the background). Taking the natural logarithm of each side gives:
This equation is solved for the half-life by simplifying and taking the natural logarithm of both sides of the equation: The nuclear half-life τ is defined such that if the initial activity is A o at time t = 0, then the activity at time t = τ will be A = ❚ o and: Measurement of the nuclear half-life for an unknown sample can help with sample identification through comparison of the measured value with published values. This is defined as the time that it takes the activity to decrease by half of the original activity.
The activity of a sample can be measured as a function of time and the rate constant can be determined experimentally.Ī useful parameter in nuclear measurement is the nuclear half-life. Where A o is the initial activity of the sample at time t = 0. Since the activity of a sample, A, is proportional to the number of nuclides, N, this can be expressed as: N 0 is the number of un-decayed nuclide at time t = 0.Į is the natural exponential number (approximately equal to 2.7138). N is the number of un-decayed nuclei at time t. This can be solved using calculus to provide the following: Where λ is the nuclear decay constant that depends on the particular isotope and the type of particle that is being emitted.įor infinitesimally small times this equation may be written as: The change in the number of un-decayed nuclei, ΔN, is proportional to the number of un-decayed nuclei, N, and the time over which the change takes place, Δt: The activity of radioactive material depends upon the amount of material present and decreases with time as the nuclei decay to another state. The activity of a radioactive substance is the number of nuclei that decay (through the emission of particles) per unit time.
#Half life chemistry calculator how to
To demonstrate how to determine a half-life from decay data.
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