Question

What fraction of the 239Pu present today will be present in 1000 years if it has a half-life of 24,000 years?

a) 1/4
b) 1/8
​c) 1/16
d) 1/32

Answer 1

The fraction of

239

�

�

239

Pu present in 1000 years will be

1

/

32

1/32.

Step-by-step explanation:

The decay of

239

�

�

239

Pu follows the exponential decay formula

�

(

�

)

=

�

0

⋅

(

1

/

2

)

�

/

�

N(t)=N

0

​

⋅(1/2)

t/T

, where

�

(

�

)

N(t) is the amount of

239

�

�

239

Pu at time

�

t,

�

0

N

0

​

is the initial amount,

�

T is the half-life, and

�

t is the time elapsed. In this case, the half-life (

�

T) is 24,000 years. To find the fraction remaining after 1000 years, we use the formula:

Fraction remaining

=

(

1

2

)

1000

/

24000

=

1

32

Fraction remaining=(

2

1

​

)

1000/24000

=

32

1

​

This indicates that after 1000 years, only

1

/

32

1/32 of the original

239

�

�

239

Pu will remain.

It's crucial to note that the exponential decay model describes the decay process, where each half-life reduces the quantity by half. The given half-life of 24,000 years means that after each 24,000 years, the amount of

239

�

�

239

Pu is halved. Therefore, after 1000 years, which is less than a complete half-life, the fraction remaining is

1

/

32

1/32.

Answer 2

After 1000 years, a fraction of 1/4 of the Plutonium-239 present today will still remain, as the time elapsed is much less than one half-life period of Plutonium-239 (option a).

Step-by-step explanation:

The subject of this question is Physics, specifically focusing on the concept of the half-life of a radioactive isotope. Plutonium-239 (239Pu) is the isotope in question, with a stated half-life of 24,000 years. To determine the fraction of 239Pu that will remain after 1000 years, we need to calculate how much of the isotope would remain after one half-life cycle proportionally to the specified duration.

The formula to calculate the remaining amount of a radioactive isotope after a certain period is:

N = N0 × (1/2)(t/T)

Where:

• N is the remaining quantity of the isotope,
• N0 is the original quantity,
• t is the elapsed time (1000 years),
• T is the half-life period (24,000 years).

To calculate the fraction remaining after 1000 years:

N = N0 × (1/2)(1000/24000)

N = N0 × (1/2)(1/24)

Because 1/24 is less than one half-life period, we know that more than half of the original amount will still be present. Since the power (1/24) is small, we do not approach a full half-life cycle, meaning the fraction remaining will be somewhat less than 1 but certainly more than 1/2. Hence, the closest answer from the options provided is:

(a) 1/4