Question

The half-life of Einsteinium-252 is 471.7 days. How many milligrams of a 100.0 mg sample would have decayed after exactly 5 half-lifes? Please show all work

Answer 1

The amount that would have decayed after exactly 5 half-lives is 96.875 mg

Step-by-step explanation

Given:

Half-life of the substance, = 471.7 days

Initial quantity of the substance = 100.0 mg

Number of half-life, n = 5

What to find:

The milligrams of the sample that would have decayed after exactly 5 half-lives.

Solution

Note that the length of the half-life played no role in this calculation.

The first step is to calculate the amount of the 100.0 mg sample remaining after 5 half-lives using the half-life formula.

`N_{t_{(1)/(2)}}=N_0((1)/(2))^{t_{(1)/(2)}}`

So the amount remaining after exactly 5 half-lives is

`=100.0mg((1)/(2))^5=100.0mg*(1)/(32)=3.125\text{ }mg`

The amount that would have decayed = Initial amount - Amount remaining after exactly 5 half-lives.

The amount that would have decayed = 100.0 mg - 3.125 mg = 96.875 mg

Therefore, The amount that would have decayed after exactly 5 half-lives is 96.875 mg