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 21.5 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

Given :-diameter for N14 is 21.5cm, so radius r₁= 0.1075 m For the circular motion, the centripetal forcefis the magnetic force so:

mv²/r = Bqv

r = mv²/(Bq)

For the N14 particle:

r₁= (2. 32×10^-26) *8950*8950/(B * 1.6x10^-19)

0.1075=B*2.32*895*895*1.6*10^(-26-19+2)

^B=3.57*1035T

For the N15 particle:

r_{2= 2.49*10^-26*8950*8950*3.57*10³⁵*1.6*10^-19}

^{_=11.39*10(6-26+35-19+2)}

^=11.39*10-2

^{r₂ = 0.114 m}

^{The separation is the difference in diameters which is}

2r₂ - 2r₁ = 2(r₂ - r₁).

=2(0.114- 0.1075)

=2*0.0065

=0.013 m Ans.