Question

If you have 40 milligrams of uranium-232 that has a half-life of 70 years, how much of uranium-232 will remain in 140 years?

Answer 1

It will take 210 years.

Explanation:
The formula for radioactive decay is

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
a
a
N
N
0
=
(
1
2
)
n
a
a
∣
∣
∣
−−−−−−−−−−−−−−−−−



where

N
0
=
original amount of isotope

N
=
amount of isotope remaining

n
=
number of half-lives

and

n
=
t
t
½

where

t
=
the time for the decay

t
½
=
the half-life

In your problem,

N
0
=
10 g

N
=
1.25 g

t
½
=
70 years

N
N
0
=
(
1
2
)
n

1.25
g
10
g
=
(
1
2
)
n

1
8
=
1
2
n

n
=
3

So, the uranium has decayed for 3 half-lives.

n
=
t
t
½

t
=
n
t
½
=
3 × 70 years
=
210 years