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.