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half life of radioactive elements, Study notes of Nuclear Physics

halflife of radioactive elements definiton and formula

Typology: Study notes

2022/2023

Available from 10/04/2023

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Half life of radioisotopes
Half-life, in radioactivity, the interval of time required for one-half of the
atomic nuclei of a radioactive sample to decay or, equivalently, the time
interval required for the number of disintegrations per second of a
radioactive material to decrease by one-half.
Let N be the size of the population of the radioactive atoms at a given time t,
dN be the amount by which it decreases in time dt. The rate of change is given
as dN/dt = -λN, where λ is the decay constant.
N = N0 e-λt
N0 = Initial number of radioactive atoms at t = 0
the population decays exponentially at a rate that depends on decay
constant. The time taken for half of the radioactive atoms to decay is called
the half-life.
N = N0e- λt
if T is the half life then, T = t
N = N0/2
Substituting we get,
N0/2 = N0 e- λt
½ = e- λt
2 = e λt
Loge 2 = λ T
0r
T= 0.693/ λ
The half life of a radioactive element is inversely proportional to the decay
constant of that element.
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Half life of radioisotopes Half-life , in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay or, equivalently, the time interval required for the number of disintegrations per second of a radioactive material to decrease by one-half. Let N be the size of the population of the radioactive atoms at a given time t, dN be the amount by which it decreases in time dt. The rate of change is given as dN/dt = - λN, where λ is the decay constant. N = N 0 e-λt N0 = Initial number of radioactive atoms at t = 0 the population decays exponentially at a rate that depends on decay constant. The time taken for half of the radioactive atoms to decay is called the half-life. N = N 0 e-^ λt if T is the half life then, T = t N = N0/ 2 Substituting we get, N0/2 = N 0 e-^ λt ½ = e-^ λt 2 = e λt Loge 2 = λ T 0r T= 0.693/ λ The half life of a radioactive element is inversely proportional to the decay constant of that element.

Half life value of some important radioisotopes,  Americium- 241 432.2 years  Lutetium- 177 6.71 days  Barium- 133 10.74 years  Molybdenum- 99 66 hours  Calcium- 45 163 days  Phosphorus- 32 14.29 days  Phosphorus- 33 25.4 days  Cadmium- 109 464 days  Carbon- 14 5730 years  Plutonium- 239 24,065 years  Cesium- 137 30 years  Polonium- 210 138.38 days  Cobalt- 60 5.271 years  Selenium- 75 119.8 days  Hydrogen- 3 12.35 years  Indium- 111 2.83 days  Technetium- 99 213,000 years  Technetium- 99m 6.02 hours  Iodine- 131 8.04 days  Xenon- 127 3 6.41 days  Iodine- 129 15,700,000 years  Iodine- 125 60.14 days  Uranium- 238 4,468,000,000 years  Uranium- 235 703,800,000 years