Answer :
Answer:
Step-by-step explanation:
Hydrogen-3, also known as tritium, has a half-life of approximately 12.32 years. This means that every 12.32 years, half of the tritium present will decay into helium-3.
To find out how much of a 5 gram sample of hydrogen-3 remains after 5 years, we can use the concept of half-life and exponential decay.
Determine the fraction remaining after 5 years:
The formula for radioactive decay is:
(
)
=
0
(
1
2
)
1
/
2
N(t)=N
0
(
2
1
)
T
1/2
t
where:
(
)
N(t) is the amount of substance remaining after time
t,
0
N
0
is the initial amount of substance,
1
/
2
T
1/2
is the half-life of the substance.
Given:
0
=
5
N
0
=5 grams (initial sample),
1
/
2
=
12.32
T
1/2
=12.32 years (half-life),
=
5
t=5 years.
Now, calculate
(
5
)
N(5):
(
5
)
=
5
(
1
2
)
5
12.32
N(5)=5(
2
1
)
12.32
5
Perform the calculation:
First, calculate
5
12.32
12.32
5
:
5
12.32
≈
0.4056
12.32
5
≈0.4056
Now, calculate
(
1
2
)
0.4056
(
2
1
)
0.4056
:
(
1
2
)
0.4056
≈
0.7746
(
2
1
)
0.4056
≈0.7746
Finally, multiply by the initial amount to find
(
5
)
N(5):
(
5
)
=
5
×
0.7746
≈
3.873
grams
N(5)=5×0.7746≈3.873 grams
Therefore, after 5 years, approximately
3.87
3.87
grams of the 5 gram sample of hydrogen-3 would remain. This calculation shows the application of exponential decay in determining the remaining amount of a radioactive substance after a given time period.
