Q. 64

Expert-verified
Found in: Page 834

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio . The sample is ionized, the positive ions are accelerated (starting from rest) through a potential difference , and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Consider a mass spectrometer with a magnetic field and an spacing between the entrance and exit holes. To five significant figures, what accelerating potential differences are required to detect the ions and ? See Exercise for atomic masses; the mass of the missing electron is less than and is not relevant at this level of precision. Although and both have a nominal molecular mass of , they are easily distinguished by virtue of their slightly different accelerating voltages. Use the following constants:

Part

For,the potential difference is

Part

For ,the potential difference is

Part

For ,the potential difference is

See the step by step solution

## Step: 1 Finding potential difference:

As each ion is lacking one electron, it has a positive charge of magnitude . At the entry hole to the area with uniform magnetic field, the work done by the electric force is transformed to the kinetic energy of the ion:

Because the magnetic force is always perpendicular to the direction of motion, the ion's speed remains constant after it reaches the uniform magnetic field. It works as a centripetal force, bending the ion's course to be round.

where ( is the trajectory's radius and d is the diameter) such that we can write

## Step: 2 Equating the equations:

Each ion's mass in relation of atomic weight is

## Step: 3 Obtaining the values: (part a and part b and part c)

Getting potential difference by substituting the values in equation,

For ,

For ,

For ,