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Note that both N and R decrease exponentially with time The decay rate of a sample often referred to as its activity ASD 2011/12 Radioactivity and Nuclear Energy 6 / 27 PPH0105 Modern Physics and Thermodynamics 5.2.3 Half-life T1/2, time it takes half of a given number of radioactive nuclei to decay Half-life is another useful parameter in characterizing the decay of a particular nucleus.
N = N0/2, t = T1/2 N = Noe-λt N0 = N0e-λT1/2 ; eλT1/2 = 2 2 Taking the natural logarithm of both sides, we get T1 2 = ln2 λ = 0.693 λ (5.5) This is a convenient expression relating half-life to decay constant.
• γ-rays can penetrate several centimeters of lead.If we write Equation 5.1 above in the form d N N = − λ dt (5.2) We can integrate the expression to give N No ∫ d N N = −λ ∫ 0 t dt N ln = −λt No N = Noe-λt No represents the number of radioactive nuclei at t = 0.5.2.3 Decay Rate The decay rate R (the number of decays per second), can be obtained by differentiating the last equation above with respect of time: (5.3) R= d N dt λ λ = N0λe-λt = R0e-λt (5.4) where Ro = N0λ is the decay rate at t = 0 and R = λN.Understand the application of radioactivity such as carbon dating and medicine 5. Describe nuclear reactions and differentiate all of it ASD 2011/12 Radioactivity and Nuclear Energy 1 / 27 PPH0105 Modern Physics and Thermodynamics Mind Map Alpha decay Beta decay Decay process Gamma decay Exponential decay equation Decay rate Type of radiation Isotopes Radioactivity Atomic and mass number Radioactivity and Nuclear Energy Carbon dating Application Medicine Chain reaction Nuclear reaction Proton Nucleus Neutron Binding energy Rutherford’s Alpha Scattering Experiment Fusion Fission Einstein’s equation ASD 2011/12 Radioactivity and Nuclear Energy 2 / 27 PPH0105 Modern Physics and Thermodynamics 5.1 Atomic and Mass Number All nuclei are composed of two types of particles: protons and neutrons.(Except for ordinary hydrogen nucleus since it has only a single proton).
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The results showed that Ötzi died over 5000 years ago, sometime between 33 BC. Uranium has a very long half-life and so by measuring how much uranium is left in a rock its approximate age can be worked out.