The half-life of iodine-123 is about 13 hours. beginning with 50 grams: a) write an equation that gives the amount of iodine-123remaining after t hours. b) determine the number of hours needed for your sample todecay to 10 grams.

Dawson Downs

Dawson Downs

Answered question

2022-07-25

The half-life of iodine-123 is about 13 hours.
beginning with 50 grams:
a) write an equation that gives the amount of iodine-123remaining after t hours.
b) determine the number of hours needed for your sample todecay to 10 grams.

Answer & Explanation

encoplemt5

encoplemt5

Beginner2022-07-26Added 15 answers

For part a,
amount left after t hours = (the amount you startedwith)*( e k t )
where t is time and k is your decay constant
Say amount of Iodine left after some time t is I(t)
so,
the equation would be: I ( t ) = 50 e k t
For part b,
You want to know t.
Plug in your values to the equation you just got:
10 grams = 50 ( e k t )
You need k. You know that half of your iodine will be gone in 13hours.
25 = 50 ( e k ( 13 ) )
So,
13 k = ln ( 1 / 2 ) = ln 2
k = ( ln 2 ) / ( 13 )
So k = -0.05332
Then, just plug back in, this time solving for t
10 = 50 ( e ( 0.05332 ) t )
e ( 0.05332 ) t = ( 10 / 50 )
e ( 0.05332 ) t = ( 1 / 5 )
( 0.05332 ) t = ln ( 1 / 5 )
So, t = 30.185 hours
Brenton Dixon

Brenton Dixon

Beginner2022-07-27Added 5 answers

Y = 50 ( 1 / 2 ) t / 13 (x is the initial amount)
10 = 50 ( 1 / 2 ) t / 13
. 2 = 1 / 2 t / 13
.2 13 = 1 / 2 t
now solve for t

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