What is the half life of a 3 g sample of radioisotope that decayed to 0.75 g in 30 days?

Answer 1

15 days

Answer 2

The half-life of a radioactive isotope that decays from 500g to 62.5g in 24.3 hours is 8.1 hours.

AT = A0 2(-T/H)

62.5 = (500) 2(-24.3/H)

0.125 = 2(-24.3/H)

log2(0.125) = -24.3/H

-3 = -24.3/H

H = 8.1

Answer 3

1.5 years

After 1 half-life, half will be remaining: 500 - 250 = 250g

After 2 half-lives, another half of the amount will decay: 250-125 = 125

So in 2 half-lives, you have 125 grams left, which according to your problem took 3 years. So in three years you had 2 half-lives occur, therefore the half-life of the isotope is 3 yrs/2 or 1.5 years. Hope that makes sense.

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

You can also solve it mathematically using the decay formula:

At = A0 e-kt , where k is the decay constant defined as k = ln 2 / t1/2 (half-life)

Ao = amount initially, or 500 g

At = amount after some period of time, in this case 3 years, so At = 125 g

t = time elapsed or 3 years

Substitute the numbers in the formula and solve for k

125 = 500 e-3k

e-3k = 125/500

ln {e-3k = 0.25}

-3k = ln (0.25)

k = ln (0.25)/-3

substitute into decay constant formula for k to calculate half-life:

t1/2 = ln 2 / k

= - ln(2)/[ln(0.25)*3]

t1/2 = 1.5 yrs

Answer 4

If 125g of a 500g sample remains after 30 years, then 0.25 of the original sample remains after 30 years. By inspection alone, you can see that the half-life is 15 years, i.e. after 15, 30, 45, and 60 years, you would expect 0.5, 0.25, 0.125, and 0. 0625 of the original to remain. Formally, the equation is ...

AT = A0 2(-T/H)

... where A0 is starting activity, AT is activity after some time T, and H is half-life in units of T.

Answer 5

One and a half years. If 125g is remaining then the sample's mass has undergone two half lives (from 500g to 250g then to 125g).

Answer 6

125g is 25% of 500g, 25% material remains after two half lives so half life period is 3/2 =1.5 years or 18 months.

Answer 7

28 days would be the half life because after 28 days, you have half the original mass (6 g is 1/2 of 12 g).

Answer 8

1.5 years

Answer 9

15 days.