experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment . if half life is 1590 years what percentage will disappear in one year?
To determine the percentage of radium that will disappear in one year, we can use the concept of half-life.
The half-life of a substance is the amount of time it takes for half of the substance to decay or disintegrate. In this case, the half-life of radium is given as 1590 years.
The relationship between the half-life and the rate of decay is exponential. We can use the formula:
N(t) = N₀ * (1/2)^(t/T)
Where:
N(t) is the amount of radium present at time t
N₀ is the initial amount of radium present
t is the time elapsed
T is the half-life of radium
Given that we want to find the percentage of radium that will disappear in one year, we can substitute the given values into the formula:
N(t) = N₀ * (1/2)^(1/1590)
Since N₀ represents the initial amount of radium present, we can assume it to be 100% or 1 in decimal form.
N(t) = 1 * (1/2)^(1/1590)
Calculating this expression, we find:
N(t) ≈ 0.999625
Therefore, approximately 0.999625 or 99.9625% of the radium will disappear in one year.
A(t)=Ao*(1/2)^(t/1590)
A(t)/Ao=.5^1/1590 =
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.5^1/1590 =