Polonium-218 has a half-life of about 3 minutes. After 15 minutes, how many milligrams of a 120 mg sample will remain? A. 1.875 mg B. 3.75 mg C. 4.8 mg D. 7.5 mg

Question

asked Oct 14, 2018 62.5k views

2 Answers

Ahmed Mostafa · Answer 1 · 2018-10-19T20:59:25+0000

Answer:

Option B - 3.75 mg

Explanation:

Given : Polonium-218 has a half-life of about 3 minutes.

To find : After 15 minutes, how many milligrams of a 120 mg sample will remain?

Solution :

Considering an exponential model,

y=a_0(x)^(t)/(n)

Where, y is the total amount

a_0 is the original amount
a_0=120

x is the half-life of Polonium-218
x=(1)/(2)=0.5

t is the time taken t=15 minutes

n is the time spent n=3 minutes

Substitute the values in the exponential model,

$y=120(0.5)^{(15)/(3)}$

y=120(0.5)^5

y=120(0.03125)

y=3.75

Therefore, Option B is correct.

3.75 mg is required amount.