Manganese-58 has a half-life of about 3 seconds. If you have a 90.0 gram sample, how
long would you expect it to take to decay to approximately 1.40 grams?

18.018 seconds.

Explanation:

Given that the half life of Manganese, Mn = 3 seconds. The initial sample mass = 90.0 gram, the final sample mass = 1.40 gram.

The general idea to the question is to look for the time it will take to decay from the initial mass that is 90 gram to 1.40 gram.

Therefore, we will be making use of the formula below;

J(t) = J(o) × (1/2)^t/t(hL).

Where t(hL) is the half life, t is the time taken, J(t)= mass after time,t and J(o) is the initial mass. So, let us slot in the values into the equation above.

1.4 = 90 × (1/2)^ t/3.

1.4/90 = (1/2)^t/3.

t/3 = log(0.5) (1.4/90).

+Please note that the 0.5 of the log is at the subscript).

That is the base 0.5 logarithm of (1.4/90) 0.01556 is 6.0060141295.

t = 3 × 6.0060141295.

t = 18.018 seconds.

it means there are 3 atoms of oxygen