Question

A sample contains 36 g of a radioactive isotope. How much radioactive isotope remains in the sample after 3 half-lives?

A. 12 g
B. 18 g
C. 4.5 g
D. 9 g

Answer 1

Answer:
4.5g

Explanation:

No = 36g Let half life is T

T= 3 T n number of half lives = t/T=3

N/No= (1/2)^n

Where, No be the initial amount

N be the amount left

n be the number of half lives

N/36 = (1/2)^3

N/36 = 1/8

N = 36/8 = 4.5g

Answer 2

Option "C": "4.5 g"

Step-by-step explanation:

N0 = 36 g, Let half-life is T.

t = 3 T, n is number of half lives = t / T = 3

By using the decay law of radioactivity

N / N0 = (1 / 2)^n

where

"N0" be the "initial amount"

"N" be the "amount left"

"n" be the "number of half-lives"

N / 36 = (1/2)^3

N / 36 = 1 / 8

N = 36 / 8 = 4.5 g