The half-life of carbon-14 is 5,730 years. How many grams of parent material will remain from a 120-gram sample of carbon-14 after 2 half-lives?
A. 90
B. 60
C. 30
D. 15
Answer (3)
t 2 1 = 5730 N 0 = 120 g t = 2 t 2 1 = 2 ⋅ 5730 = 11460 N ( t ) = ? N ( t ) = N 0 ( 2 1 ) t 2 1 t N ( 11460 ) = 120 ⋅ ( 2 1 ) 5730 11460 N ( 11460 ) = 120 ⋅ ( 2 1 ) 2 N ( 11460 ) = 120 ⋅ 4 1 N ( 11460 ) = 30 g
After one half-life . . . 1/2 of the total parent material
After another half-life . . . 1/2 of the half remains = 1/4 of the total original parent
If the original parent is 120 grams, then (1/4 x 20) = 30 grams remains after 2 half-lives. It makes no difference what the substance is, or how long its half-life is.
After 2 half-lives of carbon-14, which lasts 5,730 years each, 30 grams will remain from an initial sample of 120 grams. The answer is C. 30 grams.
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