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Logarithms: radioactivity and applications to the human body


Mean lifetime t½

The term Mean lifetime refers to the time required for the decaying quantity of a radioactive sample to fall to one half of its initial value of radiation.

C-14


t½ for Molybdenum - 99 (used as a tumor marker)

Time (h)


t ½ for Uranium - 238 (Radioactive waste)

years


T

½

= 28,8 years

t ½ for Strontium - 90 (Radioactive waste)


Equation of Mean lifetime

( )

N 0 0,693. t ln = N t1

● ● ● ● ●

2

t ½ : mean lifetime No : initial quantity of the sample N : quantity that remains at time t t: running time 0,693: Ln 2


Aplications in Medicine (radiotherapy) Element

Mean timelife

Area of body that describes

I

8.1 días

Thyroid gland

59

Fe

45.1 días

Red blood cells

99

Mo

67 horas

Metabolism

P

14.3 días

Eyes, liver, tumors

51

Cr

27.8 días

Red blood cells

87

Sr

2.8 horas

Bones

99

To

6.0 horas

Heart, bones, liver, lungs

133

Xe

5.3 días

24

Na

14.8 horas

131

32

Lungs Circulatory system


Radioactive dating processes - Based in Carbon 14: aplications in arqueology and antropology t1/2 = 5.730 years - Based in Uranium 238: aplications in geology and minery. t1/2 = 4,5x109 years


Radioactive dating processes - Based in Carbon 14: aplications in arqueology and antropology t1/2 = 5.730 years - Based in Uranium 238: aplications in geology and minery. t1/2 = 4,5x109 years


A fossil was found with a 10% of C-14 in relation with the alive sample, so... this fossil is 19.138 years old.

Why?


Logarithms