Manganese-56 is a beta emitter with a half-life of 2.6 hr. What is the mass of manganese-56 in a 49.7-mg sample of the isotope after 10.4 hr?

3.11 mg

Explanation:

From the question given above, the following data were obtained:

Half-life (t½) = 2.6 hr

Original amount (N₀) = 49.7 mg

Time (t) = 10.4 hr

Amount remaining (N) =.?

Next, we shall determine the number of half-lives that has elapsed. This can be obtained as follow:

Half-life (t½) = 2.6 hr

Time (t) = 10.4 hr

Number of half-lives (n) =?

n = t / t½

n = 10.4 / 2.6

n = 4

Thus, 4 half-lives has elapsed.

Finally, we shall determine the amount remaining. This can be obtained as illustrated below:

Original amount (N₀) = 49.7 mg

Number of half-lives (n) = 4

Amount remaining (N) =.?

N = 1/2ⁿ × N₀

N = 1/2⁴ × 49.7

N = 1/16 × 49.7

N = 0.0625 × 49.7

N = 3.11 mg

Therefore, the amount remaining is 3.11 mg

the answers would be

the first one and the second one