the half-life of a radium is 1690 years is 90 grams is present now, how much will be present in 70 years
(90 g)* 2^(-70/1690)
= 90g * 0.9717 = 87.5 g
To calculate the amount of radium that will be present in 70 years, we can use the formula for exponential decay:
N(t) = N0 * (1/2)^(t / T)
Where:
N(t) = the amount of radium at time t
N0 = the initial amount of radium
t = the time elapsed
T = the half-life of the radium
In this case:
N0 = 90 grams (initial amount)
t = 70 years (time elapsed)
T = 1690 years (half-life)
Let's substitute the values into the formula and calculate:
N(70) = 90 * (1/2)^(70 / 1690)
N(70) ≈ 90 * (0.5)^(0.0414)
N(70) ≈ 90 * 0.9336
N(70) ≈ 84.0224
Therefore, approximately 84.02 grams of radium will be present after 70 years.
To calculate the amount of radium present after a certain time using its half-life, you can use the following equation:
N = N₀ * (1/2)^(t / T)
Where:
N = final amount of radium
N₀ = initial amount of radium
t = time passed since the initial amount (in this case, 70 years)
T = half-life of radium (in this case, 1690 years)
First, we need to find the initial amount of radium. From the information given, we know that 90 grams are present at the beginning (N₀ = 90g).
Now we can substitute these values into the equation and solve for N:
N = 90 * (1/2)^(70 / 1690)
N = 90 * (1/2)^(0.0414)
N ≈ 90 * (0.9959)
N ≈ 89.63 grams
Therefore, after 70 years, approximately 89.63 grams of radium will be present.