An unknown radioactive element decays into non-radioactive substances.

Answered question

2022-05-09

An unknown radioactive element decays into non-radioactive substances. In 780 days, the radioactivity of a sample decreases by 59 percent.

 

(a) What is the half-life of the element?
half-life:    (days)
Round to two decimal places.

(b) How long will it take for a sample of 100 mg to decay to 47 mg?
time needed:    (days)
Round to two decimal places.
 

Answer & Explanation

star233

star233

Skilled2022-05-13Added 403 answers

Govering equation: A=A0ekt (1)

where A0 is the amount of the element at t=0

Now, when t=780A=41100A0

So, 41100A0=A0e780k

e780k=41100

780k=ln(41100)

 

k=1780ln(41100)

k=0.00114307

So, (1) becomes A=A0e0.00114307

a) Let when t=T,A=A02

Then e0.00114307T=12

0.00114307T=ln(2)

T=ln(2)0.00114307=606.4

So, the half-life of the element is 606.4 days

b) Let T' be the time taken by a sample of 100 mg to decay to 47 mg.

Then

47100=e-0.00114307T'

-0.00114307T'=ln(10047)

T'=ln(10047)0.00114307=660.5

 

Hence, the time required to decay to 44 mg is 606.5

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