17) The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is about

Question

17) The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is about 29 years. Suppose you have samples of both isotopes, and that they initially contain equal numbers of atoms of these isotopes. How will the activities (number of decays per second) of the samples compare?

A) The activity of the cobalt-60 sample will be greater.

B) The activities cannot be compared without more information.

C) The activities will be equal.

D) The activity of the strontium-90 sample will be greater.

If you have 20 gram of Cobolt-60, how much is decayed after 50 Year? What about Strontium-90?

Explanation / Answer

half life of cobalt = 5.3 yr

half life of Strontium = 29 yr

from above it is clear cobalt has shorter half life than Strontium. Shorter half life means more decay per unit time ,which means higher activity,if the number of atoms are same.

hence cobalt activity will be greater. (A)

------------------------------------------------------------

n = no of half lives

N0 = total no of atoms present originally

N = total no of atoms left undecayed.

n = no of half lives in 50 yr = 50 yr / 5.3 yr

= 9.43

from N = N0 ( 1/2)n

= 20*(1/2)9.43

= 0.0289 gm

so decayed will be = 20 - 0.0289 = 19.971gm

for Stronium:

n = 50/ 29 = 1.72

N = 20*( 1/2)1.72

= 6.07 gm

decayed = 20 - 6.07 = 13.93 gm

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