ÿþ3 1 . ( a ) T h e h a l f - l i f e T 1 / 2 a n d t h e d i s i n t e g r a t i o n c o n s t a n t a r e r e l a t e d b y T 1 / 2 = ( l n 2 ) / », s o T 1 / 2 =
( l n 2 ) / ( 0 . 0 1 0 8 h - 1 ) = 6 4 . 2 h .
( b ) A t t i m e t , t h e n u m b e r o f u n d e c a y e d n u c l e i r e m a i n i n g i s g i v e n b y
N = N 0 e - »t = N 0 e - ( l n 2 ) t / T 1 / 2 .
W e s u b s t i t u t e t = 3 T 1 / 2 t o o b t a i n
N
= e - 3 l n 2 = 0 . 1 2 5 .
N 0
I n e a c h h a l f - l i f e , t h e n u m b e r o f u n d e c a y e d n u c l e i i s r e d u c e d b y h a l f . A t t h e e n d o f o n e h a l f - l i f e ,
N = N 0 / 2 , a t t h e e n d o f t w o h a l f - l i v e s , N = N 0 / 4 , a n d a t t h e e n d o f t h r e e h a l f - l i v e s , N = N 0 / 8 =
0 . 1 2 5 N 0 .
( c ) W e u s e
N = N 0 e - »t .
1 0 . 0 d i s 2 4 0 h , s o »t = ( 0 . 0 1 0 8 h - 1 ) ( 2 4 0 h ) = 2 . 5 9 2 a n d
N
= e - 2 . 5 9 2 = 0 . 0 7 4 9 .
N 0
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