A mass spectrometer, a device used to measeur the masses of inos, is depicted sc
ID: 1324748 • Letter: A
Question
A mass spectrometer, a device used to measeur the masses of inos, is depicted schmetacally below. And ion, of mass m and charge of magnitude q, is produced at rest by source S and then accelerated by the potential difference V. The ion then enters a chamber in which there is a uniform magnetic filed B direceted out of the page, and susbsequently travels in a semi-cirlce, striking the photographic plate a distance x away form the entry slit.
a) what is the sign of the ionss electric charge? Explain your reasoning.
b) What is the speed of the ion as it passes through the entry slit?
A mass spectrometer, a device used to measeur the masses of inos, is depicted schmetacally below. And ion, of mass m and charge of magnitude q, is produced at rest by source S and then accelerated by the potential difference V. The ion then enters a chamber in which there is a uniform magnetic filed B direceted out of the page, and susbsequently travels in a semi-cirlce, striking the photographic plate a distance x away form the entry slit. a) what is the sign of the ions½s electric charge? Explain your reasoning. b) What is the speed of the ion as it passes through the entry slit? c) Show that, in terms of the given variables, the mass of the ion can be expresses as:
Explanation / Answer
Part A)
Positive
By the right hand rule, since the force is to the right, with the firld out of the page, a positive charge will be needed for the upward travel.
Part B)
From conservation of energy PE = KE
qV = .5mv2
v = sqrt(2qV/m)
Part C)
Using r = mv/qB, we know that x = 2r, so...
x = 2mv/qB -- lets square all of this
x2 = 4m2v2/q2B2
From PE = KE where qV = .5mv2 we see that v2 = 2qV/m
Sub this v2 in above
x2 = 4m22qV/mq2B2
Simplify and get x2 = 8mV/qB2
Solve for m and get m = qB2x2/8V
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