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Manganese-56 is a β emitter with a half life of 2.6 hours. What is the mass of manganese-56 in an original 1.00mg sample after 10.4 hours?

User Jbsound
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1 Answer

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Final answer:

The mass of manganese-56 in the original 1.00mg sample after 10.4 hours is 0.0625mg.

Step-by-step explanation:

To calculate the mass of manganese-56 in the original 1.00mg sample after 10.4 hours, we first need to determine the number of half-lives that have passed. Since the half-life of manganese-56 is 2.6 hours, we divide the total time (10.4 hours) by the half-life:

Number of half-lives = Total time / Half-life = 10.4 hours / 2.6 hours = 4 half-lives

Each half-life reduces the amount of manganese-56 by half. So, after 4 half-lives, the remaining mass can be calculated as:

Remaining mass = Initial mass x (1/2)^(Number of half-lives) = 1.00mg x (1/2)^4 = 1.00mg x (1/16) = 0.0625mg

Therefore, the mass of manganese-56 in the original 1.00mg sample after 10.4 hours is 0.0625mg.

User Fabrizio Ferrari
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