i have tried 1.87 1.88 and 2.14 THIS IS THE ENTIRE QUESTION The amount of meat i
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i have tried 1.87 1.88 and 2.14 THIS IS THE ENTIRE QUESTION
The amount of meat in prehistoric diets can be determined by measuring the ratio of the isotopes nitrogen-15 to nitrogen-14 in bone from human remains. Carnivores concentrate ^15N, so this ratio tells archaeologists how much meat was consumed by ancient people. Suppose you use a velocity selector to obtain singly-ionized (missing one electron) nitrogen atoms of speed 9.05 km/s and bend them along a semicircle within a uniform magnetic field. The 14N atoms travel along a semicircle with a diameter of 22.0 cm. The measured masses of these isotopes are 2.32 times 10^-26 kg (^14N) and 2.49 times 10^-26 kg for (^15N). Part A Find the separation of the ^14N and ^15N isotopes at the detector. Express your answer in centimeters.Explanation / Answer
Diameter of path for nitrogen-14,d1=22 cm=0.22 m
Radius of path for nitrogen-14,r1=(22/2) cm=0.11 m
Diameter of path for nitrogen-15,=d2
Radius of path for nitrogen-15=r2
Velocities of both ions are same as,v=9.05 km/s=9.05*103 m/s
q=1.6*10-19 C
As nitrogen ion travel in magnetic field in circular path, so the force equation is
mv2/r=qvB
B=mv/rq
Using above result for nitrogen-14
B=(2.32*10-26)*(9.05*103)/[(1.6*10-19)*(0.11)]=0.0119 T
For nitrogen-15
r2=mv/qB=(2.49*10-26)*(9.05*103)/[(1.6*10-19)*(0.0119)]=0.1184 m
So d2=0.1184*2=0.2368 m
Hence, the separation
s=d2-d1=0.2368-0.22=0.0168 m=1.68 cm
s=1.68 cm
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