Question

The half life of a new isotope found on Mars is 2 years. It takes 10 years to get the sample back to Earth. If the astronauts started with 128g of
this new isotope how much is left when they get back to Earth?

Answer 1

Answer:

3.99 g

Explanation:

The following data were obtained from the question:

Half life (t½) = 2 years.

Original amount (N₀) = 128 g

Time (t) = 10 years

Amount remaining (N) =..?

Next, we shall determine the rate of disintegration of the isotope. This can be obtained as follow:

Half life (t½) = 2 years.

Decay constant (K) =.?

K= 0.693/t½

K = 0.693/2

K = 0.3465 year¯¹.

Finally, we shall determine the amount remaining after 10 years i.e the amount remaining when they arrive on Earth. This can be obtained as follow:

Original amount (N₀) = 128 g

Time (t) = 10 years

Decay constant (K) = 0.3465 year¯¹.

Amount remaining (N) =..?

Log (N₀/N) = kt/2.3

Log (128/N) = (0.3465 × 10)/2.3

Log (128/N) = 1.5065

Take the antilog of 1.5065

128/N = Antilog (1.5065)

128/N = 32.1

Cross multiply

128 = 32.1 × N

Divide both side by 32.1

N = 128/32.1

N = 3.99 g

Therefore, the amount remaining is 3.99 g