An isotope of gallium, 67 Ga, has an atomic number of 31 and a half-life of 78 h
ID: 1401679 • Letter: A
Question
An isotope of gallium, 67Ga, has an atomic number of 31 and a half-life of 78 hours. Consider a small mass of 3.6 grams for 67Ga which is initially pure.
Questions 3 and 6 are the ones I am struggling with!
1)
Initially, what is the half-life of the gallium?
T1/2o =
hr
Your submissions:
78
Computed value:
78
Submitted:
Tuesday, July 28 at 5:50 PM
Feedback:
Correct!
2)
Initially, what is the initial decay constant of the Ga atom in the sample?
o =
hr-1
Your submissions:
.008885
Computed value:
.008885
Submitted:
Tuesday, July 28 at 5:51 PM
Feedback:
Correct!
3)
Initially, what is the decay rate of the gallium?
Ro =
bq
Your submissions:
6.21457e20
Computed value:
6.21457e20
Submitted:
Tuesday, July 28 at 6:25 PM
Feedback:
4)
What is the half-life of the gallium after 48 hours?
T1/21 =
hr
Your submissions:
78
Computed value:
78
Submitted:
Tuesday, July 28 at 6:01 PM
Feedback:
Correct!
5)
Initially, what is the initial decay constant of the Ga atoms after 48 hours?
1 =
hr-1
Your submissions:
8.885e-3
Computed value:
8.885e-3
Submitted:
Tuesday, July 28 at 6:21 PM
Feedback:
Correct!
6)
What is the decay rate of the gallium after 48 hours?
R1 =
bq
Your submissions:
2.1577e20
Computed value:
2.1577e20
Submitted:
Tuesday, July 28 at 6:22 PM
Explanation / Answer
ans 3 )
Radioactive decay is a first order reaction. Therefore we have
dm/dt= -k*N
ln (N/N0)= -k*t
N= mass at time t;
N0= initial mass;
k= decay constant
initial = t = 0
= - k * N0 =
= 0.032 g/h^-1
ans 6 )
reamining mass at 48 hrs
ln N = -kt + lnN0
N = 2.35
rate = -k * N
rate = 0.021 gm/h^-1
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