how many half lives will it take for 50 g of 99Tc to decay to 6.25 g?
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Let n = number of half lives.
50/6.25 = 8
2^n = 8
n = ?
As-81 started as 100 g solution and was reduced by two half-lives.
As-81 started as 100 g solution and was reduced by two half-lives.
To determine the number of half-lives required for a radioactive substance to decay from one amount to another, we can use the half-life formula. First, let's understand what a half-life is.
Half-life is the time taken for half of the atoms in a radioactive substance to decay. It is a constant property unique to each radioactive isotope. For 99Tc (Technetium-99), the half-life is approximately 6 hours.
Now, let's start calculating.
1. Determine the initial number of half-lives:
To find the initial number of half-lives, we need to calculate how many times 99Tc (Technetium-99) must decay by half to reach the desired amount.
Initial mass = 50 g
Final mass = 6.25 g
Since each half-life reduces the amount by half, we can set up the equation:
Final mass = Initial mass * (1/2)^(number of half-lives)
Substituting the values:
6.25 g = 50 g * (1/2)^(number of half-lives)
2. Solve for the number of half-lives:
Rearrange the equation to solve for the number of half-lives:
(1/2)^(number of half-lives) = 6.25 g / 50 g
(1/2)^(number of half-lives) = 0.125
To simplify the calculation, we can convert the decimal to a fraction:
(1/2)^(number of half-lives) = 1/8
Now, we need to find out to which power 1/2 must be raised to obtain 1/8. By inspection, we can see that 1/8 is equal to (1/2)^3.
Therefore, the number of half-lives required is 3.
Thus, it will take 3 half-lives for 50 g of 99Tc to decay to 6.25 g.