Mass spectrometer A mass spectrometer is a tool used to determine accurately the
ID: 1793520 • 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 1C to C depends on how old the material is, which is the basis for carbon-14 dating. c is continually produced in the upper atmosphere by nuclear reactions caused by "cosmic rays (high-energy charged particles from outer space, mainly proon), and C is radioactive with a half-life of 5700 years. Whena cotton plant is growing, some of the COz it extracts from the air to build tissue contains C which has diffused down from the upper atmosphere. But after the cotton has been harvested there is no further intake of c from the air, and the cosmic rays that create C in the upper atmosphere can't penetrate the atmosphere and reach the cloth. So the amount of C in cotton cloth continually decreases with time, while the amount of non-radioactive C remains constant. Here i a particular kind of mass pectrometer ( the figure). Carbon from the sample is ionized in the ion source at the left. The resulting singly ionizedc and ons have negligibly small initial velocities (and can be considered to be at rest . They are accelerated through the potential difference 1. They then enter a region where the magnetic field has a foed magnitude B-0.16 T. The 'ons pass through electric deflection plates that are 1 cm apart and have a potential difference AV2 that is adjusted so that the electric deflaction and the magnetic deflection cancel each other for a particular isotope: one isotope goes straight through, and the other isotope is deflacted 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 29 cm. There are controls that let you vary the accelerating potential V, and the deflection potential in order that only c ions go all the way through the system and reach the detector. You count each kind of ion for fioxed 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 plates; AVI detector Deflection plates; V2 lon E r isotope is deflected t this rExplanation / Answer
in magnetic field, for circular path
q v B = m v^2 / r
v = q r B / m
and E = v B , E = V2 / d
V2 = v d B = q r d B^2 / m
for 12 C :
V2 = (1.6 x 10^-19) (0.29/2) (0.01) (0.16^2) / (12 x 1.67 x 10^-27)
V2 = 296.4 Volt
for 14 C : V2 = 254 Volt
for V1: KE = q deltaV
m v^2 /2 = q V1
m (q r B / m)^2 = 2 q V1
V1 = q r^2 B^2 / 2 m
V1 for 12C = 2149 Volt
V1 for 14c = 1842 Volt
(B) V1 = 2149 V
V2 = 296.4 V
(C) V1 = 1842 V
V2 = 254 V