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the half-life of uranium-232 is 69 years. If the nuclear byproduct contains uranium-232, it is not considered safe for human contact until 99.2% of it has been decayed. How long will this take

Respuesta :

After 69 years, 50% of the element has decayed
After 1 year, then,
x = 0.5/69 = 0.00724
0.724% of uranium-239 has been decayed.
To find how long it will take for 99.2% of the element to decay, we can use a similar method:
x years/0.992 = 69 years/0.5
x = 136.896 years
Therefore, it will take 136.896 years for 99.2% of the nuclear byproduct to have decayed.
Let me know if you have any questions
mickymike92

It will take approximately 480 years for 99.2% of uranium-232 to decay.

The formula of radioactive half-life = [tex]\frac{N}{N₀} = (\frac{1}{2})^{n}[/tex]

Where N = amount of isotope remaining

N₀ = original amount of isotope

n = number of half-lives

From the given values:

N = 100 5 - 99.2%

N = 0.8 % = 0.008

N₀ = 100% = 1

Substituting to find n

0.008/1 = (1/2)ⁿ

㏒₁₎₂0.008 = n

n = ㏒0.008/㏒(1/2)

n = 6.96

Therefore, number of half-lives n = 6.96

One half-life = 69 years

6.96 half-lives = 6.96 * 69 = 480.24 years

Therefore, it will take approximately 480 years for 99.2% of uranium-232 to decay.

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