How much time in years would be required for a quantity of 1.3 kg to be reduced to 75g if the half life of cobalt-60 is 5.272 years?

Answer 1

The radionuclide 60Co27 has a half-life of about 5.3 years. That means that one half of the material will be present after 5.3 years, one quarter after 10.6 years, one eight after 15.9 years, etc. Since this is a logarithmic scale, it will take theoretically infinite time for it to decay completely away. In practice, however, it depends on the sensitivity and criteria of your measurement. If you want to consider "complete decay" to be 99.9 percent, then it would take about 10 half-lifes or 52.8 years.

AT = A0 2(-T/H)

0.001 = (1) 2(-T/5.3)

log 0.001 = -T/5.3

-9.97 = -T/5.3

T = 52.8

Answer 2

It depends on what you mean by effective zero. Cobalt-60, or any other radioactive isotope for that matter, will never completely decay to zero because the half-life equation is logarithmic.1 The equation of half-life decay is ...

AT = A0 2(-T/H)

... so pick a point that you call zero. Lets say you choose 0.00001 pounds. Plug the numbers in and solve for T ...

0.00001 = (100) 2(-T/5.3)

0.0000001 = 2(-T/5.3)

log2 (0.0000001) = -T/5.3

-23.253 = -T/5.3

T = 123.24 years, or 23.25 half-lives

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1Well, not quite, because the atoms have a finite size, and eventually you will reach a point where you cannot subdivide the atom. At that point, you will reach true zero. The issue here, however, is that will be a long time. Yes, you could calculate that, if you know the mass of the Cobalt-60 atom. I will leave that exercise to you - its the same thing as what I did above, but with a different AT.

Answer 3

Only one-quarter of the original mass will remain. A formula is M(t) = M(0) x (1/2)t/h where M(0) is the original mass, t is the time, and h is the half-life of the substance.

Answer 4

32 years is 6.09 half-lives, so the amount that remains will be the inverse of 2 to the power of 6.09.

75 * 2^-6.09 = about 1.1 grams.

Answer 5

taking that (done in my head) it goes to over 1/16 half life over 4 times, id say 23 years roughly. Sorry, no calculator

Answer 6

double halved = quartered in 2*5.3 = 10.6 yr.

Answer 7

Start: 32 g

6-mo: 16 g

1-yr: 8 g

1.5 yr: 4 g

2 yr: 2 g

...or 5th root of 32 is another way to do it.

Answer 8

1/16

Answer 9

one-quarter

Answer 10

0.63 g