Question

A mass spectrograph is used to measure the masses of ions, or to separate ions of different masses. In one design for such an instrument, ions with mass m and charge q are accelerated through a potential difference V. They then enter a uniform magnetic field that is perpendicular to their velocity and are deflected in a semicircular path of radius R. A detector measures where the ions complete the semicircle and from this it is easy to calculate R

Suppose the beam consists of a mixture of 12C and 14C ions. If V and B have the same values as in part A, calculate the separation of these two isotopes at the detector.

Answer 1

In a mass spectrograph, the separation between 12C and 14C isotopes is 2 mass units at the detector.

In a mass spectrograph, ions with different masses are separated based on their deflection in a uniform magnetic field. The separation of isotopes can be calculated by considering the mass-to-charge ratio (m/z) of each isotope.

Given that the beam consists of a mixture of 12C and 14C ions, we need to calculate the separation between these two isotopes at the detector.

1. Determine the mass-to-charge ratio (m/z) for each isotope:

- For 12C, m/z = mass/charge = 12/1 = 12

- For 14C, m/z = mass/charge = 14/1 = 14

2. Since the charge (q) is the same for both isotopes, the separation will depend on the ratio of their masses (m):

- Separation = (mass of 14C - mass of 12C) / charge

3. Calculate the separation:

- Separation = (14 - 12) / 1 = 2 / 1 = 2

Therefore, the separation between the 12C and 14C isotopes at the detector will be 2 mass units.