Radioactive isotope Berkelium-247 decays exponentially. If the continuous decay rate is 50% per thousand years and the current mass is 697.30 grams, what will the mass be 5 thousand years from now?

Answer 1

To solve this problem, we can use the exponential decay formula:

\[ A(t) = A_0 * e^{rt} \]

where:
- \( A(t) \) is the amount of substance remaining after time \( t \)
- \( A_0 \) is the initial amount of substance
- \( r \) is the decay rate
- \( t \) is the time elapsed

Given that the continuous decay rate is 50% per thousand years, we can find the decay constant as follows:

\[ r = \ln(0.5) / 1000 = -0.000693 \]

Now, let's plug in the values into the equation:

\[ A(5000) = 697.30 * e^{-0.000693 * 5000} \]
\[ A(5000) = 697.30 * e^{-3.465} \]
\[ A(5000) ≈ 697.30 * 0.03157 \]
\[ A(5000) ≈ 22 \, \text{grams} \]

Therefore, the mass of Berkelium-247 will be approximately 22 grams 5 thousand years from now.