Answer: 46.39 grams of radium
Explanation:
We can use the half-life formula to solve this problem:
A = A₀(1/2)^(t/t₁/₂)
where:
A₀ = initial amount (present)
A = final amount (in 710 years)
t = time elapsed (710 years)
t₁/₂ = half-life (1690 years)
First, we need to calculate the number of half-lives that will occur in 710 years:
n = t / t₁/₂
n = 710 / 1690
n ≈ 0.42
This means that in 710 years, the amount of radium will be reduced to half its current amount (1/2). And then reduced to half again (1/2 * 1/2) in another 1690 years.
Now we can calculate the final amount of radium after 710 years:
A = A₀(1/2)^n
A = 70(1/2)^0.42
A ≈ 46.39 grams
Therefore, after 710 years, approximately 46.39 grams of radium will be left.