An isotope of gallium, ^{67}Ga, has an atomic number of 31 and a half-life of 78 hours. Consider a small mass of 3.9 grams for ^{67}Ga which is initially pure.
1) Initially, what is the half-life of the gallium?
T_{1/2o} =
2) Initially, what is the initial decay constant of the Ga atom in the sample?
λ_{o} =
3) Initially, what is the decay rate of the gallium?
R_{o} =
4) What is the half-life of the gallium after 24 hours?
T_{1/21} =
5) Initially, what is the initial decay constant of the Ga atoms after 24 hours?
λ_{1} =
6) What is the decay rate of the gallium after 24 hours?
R_{1} =
1) Initial t1/2=78hrs
2)initial decay constant=0.693/t1/2
=0.693/78
=0.0089/hr or
32.04/sec
3)decay rate = decay constant*number of particles
=(0.0089*3.9*6.023*10^{23})/67
=3.12*10^{23}particles per hr
Or 3.024*10^{16} Cu
4)Half life remains same after 24 hrs
5)Decay constant remains same after 24 hrs
6)decay rate= decay constant *no. of particles
The math is attatched as an image
An isotope of gallium, 67Ga, has an atomic number of 31 and a half-life of 78...
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