Chapter 27, Problem 27.78P

DATA You are using a type of mass spectrometer to measure charge-to-mass ratios of atomic ions. In the device, atoms are ionized with a beam of electrons to produce positive ions, which are then accelerated through a potential difference V. (The final speed of the ions is great enough that you can ignore their initial speed.) The ions then enter a region in which a uniform magnetic field $\stackrel{\to }{\text{B}}$ is perpendicular to the velocity of the ions and has magnitude B = 0.250 T. In this $\stackrel{\to }{\text{B}}$ region, the ions move in a semicircular path of radius R. You measure R as a function of the accelerating voltage V for one particular atomic ion:

(a) How can you plot the data points so that they will fall close to a straight line? Explain. (b) Construct the graph described in part (a). Use the slope of the best-fit straight line to calculate the charge-to-mass ratio (q/m) for the ion. (c) For V = 20.0 kV, what is the speed of the ions as they enter the $\stackrel{\to }{\text{B}}$ region? (d) If ions that have R = 21.2 cm for V = 12.0 kV are singly ionized, what is R when V = 12.0 kV for ions that are doubly ionized?