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Radiocarbon Dating

The half-life...

Question

The half-life of substances X is 45 years, and it decomposes to substance Y. A sample from a meteorite was taken which contained $1.5 %$ of X and $13.5 %$ of Y by a quantity of a substance. If substance Y is not normally found on a meteoride, what is the approximate age of the meteorite?

A

270 years

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B

140 years

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C

90 years

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D

45 years

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Solution

The correct option is B 140 years
$\begin{matrix} A c c o r d i n g t o q u e s t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . i f i t i s, t h e n y o u a s s u m e t h a t t h e o r i g i n a l p e r c e n t a g e o f X i n t h e m e t e o r i t e w a s, \Rightarrow 15 p e r c e n t (s i n c e 1.5 + 13.5 = 15) . I f o n l y 1.5 p e r c e n t r e m a i n e d o f X, y o u s h o u l d k n o w t h a t 10 p e r c e n t o f t h e o r i g i n a l m a s s h a d d e c a y e d . \Rightarrow 100 d o w n t o 50 t h a t^{'} s o n h a l f - l i f e (45 y e a r s) \Rightarrow 50 d o w n t o 25 t h a t^{'} s t w o h a l f - l i v e s (90 y e a r s) \Rightarrow 25 d o w n t o 12.5 t h a t^{'} s t h r e e h a l f - l i v e s (135 y e a r s) \Rightarrow 12.5 d o w n t o 6.25 t h e r e^{'} s f o u r h a l f - l i v e s (180 y e a r s) \Rightarrow 10 p e r c e n t i s b e t w e e n 12.5 a n d 6.25 a n d i t^{'} s c l o s e r t o 12.5, s o t h i s s h o u l d h i n t y o u t h a t y o u r a n s w e r h a s t o b e b e t w e e n 135 - 180, a n d i t^{'} s c l o s e r t o 135 t h a n i t^{'} s t o 180 = 140 y e a r s . T h e r e f o r e, c o r r e c t a n s w e r C i s t h e m o s t p l a u s i b l e . \end{matrix}$

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