Question

For a mass spectrometer that has a path radius of 12.5 cm for singly ionized 12C atoms (mass 1.99×10-26kg), find the separation of the 14N (mass 2.32×10-26kg) and 15N (mass 2.49×10-26kg) isotopes at the detector. The separation of the isotopes at the detector is 2(ra-rb).

Answer 1

The separation of the 14N and 15N isotopes at the detector in the mass spectrometer is 9.6 cm.

Step-by-step explanation:

In a mass spectrometer, the separation of isotopes is determined by the difference in their masses and the strength of the magnetic field. The formula for the separation of isotopes at the detector is 2(ra-rb), where ra and rb are the respective path radii of the two isotopes. For the given question, the path radius for the 12C isotope is 12.5 cm. To find the separation of the 14N and 15N isotopes, we need to calculate their respective path radii and substitute the values in the formula.

First, we find the path radius for the 14N isotope. We can use the formula r = mv/(Bq), where r is the path radius, m is the mass, v is the velocity, B is the magnetic field, and q is the charge. Substituting the values, we get r = (2.32x10^-26 kg)(3.00x10^5 m/s)/(0.250 T)(1.6x10^-19 C). Simplifying, we find r = 16.235 cm.

Next, we find the path radius for the 15N isotope. Using the same formula and substituting the values, we get r = (2.49x10^-26 kg)(3.00x10^5 m/s)/(0.250 T)(1.6x10^-19 C). Simplifying, we find r = 17.3 cm.

Finally, we substitute the values of ra and rb in the formula for separation: 2(ra-rb) = 2(17.3 cm - 12.5 cm) = 9.6 cm.