aments that appear in the same column of the periodic taole often share similar

Question

aments that appear in the same column of the periodic taole often share similar chemical properties. In the case of the alkaline earth metals, this is troublesome since the body treats calcium (necessary for proper bone growth) and radium (a radioatictive element) as chemically similar, storing both in bone marrow. The radium then bombards nearby bone cells with alpha particles, causing them to "crumble." Radium poisoning investigations often center on the identification of radium and its isotopes in bone samples using a mass spectrometer. Pictured is a schematic of a simplified mass spectrometer, showing the paths of calcium, barium (another alkaline earth metal) and radium isotopes entering the chamber. The region shown is immersed in a constant magnetic field of 0.652 tesla pointing out of the plane of the schematic. Motion of the positively-charged isotopes toward the right was initiated by a charge separation of 2464 volts on the two plates shown. Using the data shown in the table below, calculate the path radius of the Ca^+ ion. Note that 1 amu = 1.661 Times 10^-27 kg and 1 e = 1.602 Times 10^-19 C.

Explanation / Answer

apply centripetal force = magnetic force

i.e mv^2/r = qvB,

so speed v = sqrt(2eV/m)

v = sqrt(2 * 20*1.6e-19 * 2464)/(40 *1.67 e-27)

v = 4.858 *10^5 m/s

where m = mass o the charged particle

v = velocity, r = radius ,

q = charge = 1.6*10^-19 C

B = magnetic field

so now , so as r = mv/qB

mass of Ca+ is 40 u

so r = (40*1.67 e-27 * 4.858 e 5)/(20*1.6 e -19 * 0.652)

r = 0.0155 0r 1.5 cm

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