Actinium-226 has a half-life of 29 hours. If 100 mg

Jason Yuhas

Jason Yuhas

Answered question

2021-12-28

Actinium-226 has a half-life of 29 hours. If 100 mg of actinium-226 disintegrates over a period of 58 hours, how many mg of actinium-226 will remain? Use A(t)=Cekt.

Answer & Explanation

Matthew Rodriguez

Matthew Rodriguez

Beginner2021-12-29Added 32 answers

Step 1 
The given data is: 
Half life t12=29 hours 
Initial 100 mg 
To find how many actinium-226 will remain after 58 hours. 
Step 2 
The given equation is: 
A(t)=Cekt (1) 
At t=0,A(0)=100mg 
A(0)=100 
Cek(0)=100 
C=100 
Substitute the value of C in equation (1), 
A(t)=100ekt (2) 
Step 3 
At half life t=29 hours,A(29)=1002=50mg 
A(29)=100e29k 
50=100e29k 
e29k=12 
29k=ln(0.5) 
k=0.0239 
Substitute the value of k in equation (2), 
A(t)=100e0.0239t 
Step 4 
Now find actinium-226 remain after 58 hours is, 
A(58)=100e0.0239×58 
=25mg 
Thus, the actinium remains after 58 hours is 25mg.

Jillian Edgerton

Jillian Edgerton

Beginner2021-12-30Added 34 answers

t12=29 hours
no of half lives (n) =Given fet12
n=58 hours29 hours=2
Amount left =Initial Amount2n
=100mg22=100mg4
Ac=266 remain=225mg

karton

karton

Expert2022-01-04Added 613 answers

Solution:
Using formula:
A=A0(12)yn
A is final amount after time "t".
h is the half-life
Given: A0=100mg
h=29 hours
t=58 hours
A=?
A=100mg(12)58 hours29 hours
=100mg(12)2
=100mg×14
A=25mg
25mg of actinium-226 will remain after 58 hours

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