Mass spectrometer A mass spectrometer is a tool used to determine accurately the
ID: 2301750 • Letter: M
Question
Mass spectrometer
A mass spectrometer is a tool used to determine accurately the mass of individual ionized atoms or molecules, or to separate atoms or molecules that have similar but slightly different masses. For example, you can deduce the age of a small sample of cloth from an ancient tomb, by using a mass spectrometer to determine the relative abundances of carbon-14 (whose nucleus contains 6 protons and 8 neutrons) and carbon-12 (the most common isotope, whose nucleus contains 6 protons and 6 neutrons). In organic material the ratio of 14C to 12C depends on how old the material is, which is the basis for "carbon-14 dating." 14C is continually produced in the upper atmosphere by nuclear reactions caused by "cosmic rays" (high-energy charged particles from outer space, mainly protons), and 14C is radioactive with a half-life of 5700 years. When a cotton plant is growing, some of the CO2 it extracts from the air to build tissue contains 14C which has diffused down from the upper atmosphere. But after the cotton has been harvested there is no further intake of 14C from the air, and the cosmic rays that create 14C in the upper atmosphere can't penetrate the atmosphere and reach the cloth. So the amount of 14C in cotton cloth continually decreases with time, while the amount of non-radioactive 12C remains constant.
Here is a particular kind of mass spectrometer (see the figure). Carbon from the sample is ionized in the ion source at the left. The resulting singly ionized 12C+ and 14C+ions have negligibly small initial velocities (and can be considered to be at rest). They are accelerated through the potential difference ?V1. They then enter a region where the magnetic field has a fixed magnitude B = 0.19 T. The ions pass through electric deflection plates that are 1 cm apart and have a potential difference ?V2 that is adjusted so that the electric deflection and the magnetic deflection cancel each other for a particular isotope: one isotope goes straight through, and the other isotope is deflected and misses the entrance to the next section of the spectrometer. The distance from the entrance to the fixed ion detector is a distance of w = 25 cm. There are controls that let you vary the accelerating potential ?V1 and the deflection potential ?V2 in order that only 12C+ or 14C+ ions go all the way through the system and reach the detector. You count each kind of ion for fixed times and thus determine the relative abundances. The various deflections insure that you count only the desired type of ion for a particular setting of the two voltages.
(a) Which accelerating plate is positive?
bottomtop
Which deflection plate is positive?
rightleft
What is the direction of the magnetic field inside the spectrometer?
out of pageinto page
(b) Determine the appropriate numerical values of ?V1 and ?V2 for 12C. Carry out your intermediate calculations algebraically, so that you can use the algebraic results in the next part.
?V1 = V
?V2 = V
(c) Determine the appropriate numerical values of ?V1 and ?V2 for 14C.
?V1 = V
?V2 = V
Explanation / Answer
(a) bottom/top makes no sense for the accelerating plates; the one on the left is positive, the one on the right is negative;
right/left makes no sense for the deflecting plates; the one on the top is positive, the one on the bottom is negative;
the magnetic field is into the page;
(b) we first need the velocity of the ion such that it makes the curve into the detector. From the formula for cyclotron frequency, we know v = qBr/m
The kinetic energy of the particle must equal the potential V1 times the charge so
mv2/2 = qV1
m(qBr/m)2/2 = qV1 therefore V1 = qB2r2/2m
To calculate V2, note that the magnetic force qvB must equal the electric force qV2/d where d is the plate separation so V2 = qB2rd/m
which, for the case of carbon-12 means
V1 = (1.602 * 10-19 C)(0.19 T)2(0.125 m)2/(2 * 1.9926 * 10-26 kg) = 2267.7 V
V2 = (1.602 * 10-19 C)(0.19 T)2(0.125 m)(0.01 m)/(1.9926 * 10-26 kg) = 362.82 V
(c) plugging in the mass of carbon-14 gives
V1 = 1943.7 V
V2 = 310.99 V