A freshly prepared sample of a certain radioactive isotope has an activity of 10

Question

A freshly prepared sample of a certain radioactive isotope has an activity of 10.0 mCi. After 4.10 h, the activity is 7.80mCi.

? =
What equation describes the exponential decay of the activity? h?1 T1/2 =
The half-life is the time required for the activity to decrease by a factor of two. h A freshly prepared sample of a certain radioactive isotope has an activity of 10.0 mCi. After 4.10 h, the activity is 7.80mCi. Find the decay constant and half-life of the isotope. What equation describes the exponential decay of the activity? h?1 The half-life is the time required for the activity to decrease by a factor of two. H How many atoms of the isotope were contained in the freshly prepared sample? What is the sample's activity 30 h after it is prepared?

Explanation / Answer

a)A =A0e^(-decay constant*t)
7.8 = 10.0 * e^(-decay constant * 4.1)
=> decay constant = 0.0606h-1

T1/2 = 0.693/decay constant = 0.693/0.0606 = 11.4355 hr


b)
1 mci = 3.7*10^7 disintegration /sec
here
decay constant*no . of aoms = 10mci = 3.7*10^8
=> (0.0606/3600)*no . of aoms = 3.7*10^8
=>no . of aoms = 2.198*10^13

c)A =A0e^(-decay constant*t)
=>A = 10*e^(-0.0606*30) = 1.6235mci

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