Respuesta :
Decay constant k = [tex]\frac{0.693}{t_{1/2} }[/tex] = [tex]\frac{0.693}{5730}[/tex] = [tex]1.209[/tex] ⨉ [tex]10^{-4}[/tex]/year
The rate of counts is proportional to the number of C-14 atoms in the sample.
[tex]N_{0}[/tex]=100, N=80
The age of the sample t = [tex]\frac{2.303}{K} log(\frac{N_{0 }}N)[/tex]
t = [tex]\frac{2.303}{1.209 * 10^{-4} }[/tex] ×[tex]log\frac{100}{80}[/tex] = 1846 years
What is decay?
Radioactive decay is the process in which an unstable nucleus spontaneously loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide, transforming to an atom of a different type, named the daughter nuclide.
The three principal modes of decay are called the alpha, beta and gamma decays. We will study their differences and exact mechanisms later in the class. However these decay modes share some common feature that we describe now. What these radioactive decays describe are fundamentally quantum processes, i.e. transitions among two quantum states.
Thus, the radioactive decay is statistical in nature, and we can only describe the evolution of the expectation values of quantities of interest, for example the number of atoms that decay per unit time. If we observe a single unstable nucleus, we cannot know a priori when it will decay to its daughter nuclide. The time at which the decay happens is random, thus at each instant we can have the parent nuclide with some probability p and the daughter with probability 1 − p.
This stochastic process can only be described in terms of the quantum mechanical evolution of the nucleus. However, if we look at an ensemble of nuclei, we can predict at each instant the average number of parent an daughter nuclides.
Learn more about decay
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