Question

за період напіврозпаду радіоактивного ізотопу дорівнює 5хв. За який час із 80 г даного ізотопу залишиться 5г? ​

Answer 1

Ответ: 20 хв

Объяснение: Див. додаток

Answer 2

Radioactive Decay Calculation

To calculate the remaining amount of a radioactive isotope after a certain period of time, we can use the radioactive decay formula:

N(t) = N0 * (1/2)^(t/T)

Where: - N(t) = the amount of the isotope remaining after time t - N0 = the initial amount of the isotope - t = the elapsed time - T = the half-life of the isotope

In this case, the half-life of the isotope is 5 minutes, and we want to find out how much of the 80g of the isotope will remain after a certain time.

Calculation

Substituting the given values into the formula:

N(t) = 80g * (1/2)^(t/5min)

We want to find the time t at which the remaining amount is 5g.

Solving for t

To solve for t, we can rearrange the formula:

5g = 80g * (1/2)^(t/5min)

Taking the natural logarithm of both sides to solve for t:

ln(5g/80g) = (t/5min) * ln(1/2)

t = 5min * ln(5g/80g) / ln(1/2)

Calculation Result

Calculating the value of t using the given values:

t ≈ 16.6 minutes

So, approximately 16.6 minutes will elapse before 5g of the isotope remains.