Question

After 4797 years, how much of the original 250 g of radium-226 remains, if

the half-life of radium-226 is 1599 years? *
125 grams
62.5 grams
31.3 grams
O 75.0 grams

Answer 1

After 4797 years, approximately 31.3 grams of the original 250 g of radium-226 remains.

Step-by-step explanation:

The half-life of radium-226 is 1599 years, which means that in 1599 years, half of the original amount will have decayed. After 4797 years, which is 3 times the half-life, we can calculate the amount of radium-226 remaining.

First, we find the number of half-lives that have passed by dividing 4797 by 1599:

4797 years / 1599 years = 3 half-lives

Since we have gone through 3 half-lives, the amount remaining is:

amount remaining = original amount * (1/2)^number of half-lives

amount remaining = 250 g * (1/2)^3 = 250 g * (1/8) = 31.3 grams

Therefore, after 4797 years, approximately 31.3 grams of the original 250 g of radium-226 remains.

Answer 2

31.3grams

Step-by-step explanation:

The amount of a radioactive element that remains, N(t), can be calculated by using the formula;

N(t) = N(o) × 0.5^{t/t(1/2)}

Where;

N(t) = mass of substance remaining

N(o) = mass of original substance

t(1/2) = half-life of substance

t = time elapsed

From the provided information; N(t) = ?, N(o) = 250g, t(1/2) = 1599 years, t = 4797 years

N(t) = 250 × 0.5^{4797/1599}

N(t) = 250 × 0.5^(3)

N(t) = 250 × 0.125

N(t) = 31.25g

N(t) = 31.3grams