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 8.95 km/s and bend them along a semicircle within a uniform magnetic field. The 14N atoms travel along a semicircle with a diameter of 27.5 cm . The measured masses of these isotopes are 2.32×10−26 kg (14N) and 2.49×10−26 kg for (15N). Find the separation of the 14N and 15N isotopes at the detector.

Answer 1

Step 1: Find value of uniform magnetic field, using force balance on the 14N atoms:

Force on Nitrogen-14 ions will be:

Force due to circular motion = Force due to magnetic field

Fc = Fm

m1*V^2/R1 = q*V*B

B = m1*V/(q*R1)

m1 = mass of nitrogen-14 = 2.32*10^-26 kg

V = Speed of ions = 8.95 km/sec = 8950 m/s

q = charge on simgly-ionized atoms = +e = 1.6*10^-19 C

R1 = radius of circular path of Nitrogen-14 = diameter/2 = 27.5/2 = 13.75 cm = 0.1375 m

So,

B = 2.32*10^-26*8950/(1.6*10^-19*0.1375)

B = 9.438*10^-3 T = Uniform magnetic field

Step 2: Find out the radius of path followed by Nitrogen-15:

Since we know that:

m2*V^2/R2 = q*V*B

R2 = m2*V/(q*B)

m2 = mass of Nitrogen-15 = 2.49*10^-26 kg

R2 = 2.49*10^-26*8950/(1.6*10^-19*9.438*10^-3)

R2 = 0.1476 m = 14.76 cm

Step 3: diameter of semicircle path of Nitrogen-15 will be:

d2 = 14.76*2 = 29.52 cm

given that diameter of semicircle path of Nitrogen-14 is:

d1 = 27.5 cm

So separation between 14N and 15N isotopes will be:

d = d2 - d1 = 29.52 - 27.5

d = 2.02 cm

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