Elements that appear in the same column of the periodic table often share simila

Question

Elements that appear in the same column of the periodic table 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 radioactive 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 0.452 T pointing out of the plane of the schematic. Motion of the positively-charged isotopes toward the right was initiated by a charge separation providing 2.6703 V on the two plates shown. Using the table below (a) Find the path radius of the Ca+. Note that 1 amu = 1.661 × 10-27 kg and i e = 1.602 × 10-19 C. (b) Match the paths on the the figure to the appropriate ions. Isotope Mass Charge Ca Ca 40.1 amu+2e Ba* Ba2 137 amu 2e Ra* Ra2 226 amu +2 e Ra3226 amu +3e -isolope 40.1 amu1e 137 amu+1 e 226 amu +1e delector

Explanation / Answer

let's start with calculating the change in velocity at the exit of plates

q( Vb-Aa) = 1/2 mv^2

1.6 x 10^-19 (2.67 x 10^3) = 0.5 (40.1 x 1.661x 10^-27 ) v^2

v^2= 4.272 x 10^ -16 / ( 33.303 x 10^ -27)

v^2= 1.2827 x 10^ 10

v= 1.132 x 10^ 5 m/s

R = mv/qB= ( 40.1 x 1.661x 10^-27 ) ( 1.132 x 10^ 5) / (1.6 x 10^-19 x 0.452 ) =

R = 104.256 x 10^ -3 m apprx

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