## Half lifeN(t) = N₀(1/2)^(t/th)or N(t) = N₀2^(–t/th) N₀ is initial amount N(t) is the amount remaining after time t th is the half life time, ie, time for half the amount to decay solving for t or th, t/th = –log₂(N/N₀) Half life can also be defined as the time for the activity to fall to half it's original rate. In that case: A(t) = A₀(1/2)^(t/th) or A(t) = A₀2^(–t/th) t/th = –log₂(A/A₀) Equivalent formulas N(t) = N₀(e)^(–t/τ) τ is a positive number called the mean lifetime of the decaying quantity, th = τ ln 2 = (1/λ) ln 2 τ = th / ln2 N(t) = N₀(e)^(–λτ) λ is a positive number called the decay constant of the decaying quantity. λ = 1/τ = ln2/th Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T1/2 can be related to the half-lives t1 and t2 that the quantity would have if each of the decay processes acted in isolation: 1/T₁₂ = (1/t₁) + (1/t₂) 1 rem = 0.01 Sv = 10 mSv 1 Gy = 1 Sv = 1 J / kg Relating half life to activity
Total activity— A, is number of decays per unit time of a radioactive sample. N(t) = N₀(1/2)^(t/th) dN/dt = N₀(1/th)(1/2)^t(ln(1/2)) dN/dt = N₀(1/th)(1/2)^t(–0.6931472) put the HL in seconds, the activity, number of decays per second is A = dN = (ln(1/2))(1/th)(N₀) ## Planck's lawI(v,T) = 2 hv³ / (c²}(e^(hv/kt)–1) where I(ν,T) is the energy per unit time (or the power) radiated per unit area of emitting surface in the normal direction per unit solid angle per unit frequency by a black body at temperature T; h is the Planck constant c is the speed of light in a vacuum k is the Boltzmann constant ν is the frequency of the electromagnetic radiation T is the absolute temperature of the body ## Types of RadiationThere are 3 different types of radiation from radioactive materials. 1. alpha particles, which are basically helium nuclei. The are slow and can be stopped by a piece of aluminum foil. 2. beta particles, which are high speed electrons. They have some penetrating particle. 3. gamma rays, which are basically high energy X-rays. These are the most dangerous. ## Photon energyEnergy in one photonE is photon energy in J h is the Planck constant, 6.62607e−34 Js c is the speed of light in vacuum in m/s λ is the photon's wavelength in m f is the photon's frequency E = hc/λ or since λf = c E = hc/(c/f) = hf |
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