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 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 0.352 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 2258 volts on the two plates shown. Using the data shown in the table below, calculate the path radius of the Ca ion.

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 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 0.352 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 2258 volts on the two plates shown. Using the data shown in the table below, calculate the path radius of the Ca+ ion. Using the same data table, match the particles to their path label.

Explanation / Answer

0.5*m*v^2 = V*q

V = sqrt(2*q*V/m) =


for ca+

R1 = ((?(2*2258*1.602*10^-19*0.666*10^-25))/(1.602*10^-19*0.352) = 123.094 mm



for Ca2+

R2 = ((?(2*2258*3.204*10^-19*0.666*10^-25))/(3.204*10^-19*0.352) = 87.041 mm



for Ba+

R3= ((?(2*2258*1.602*10^-19*(2.28*10^-25))))/(1.602*10^-19*0.352) = 227.756 mm



for Ba2+

R4 = ((?(2*2258*3.204*10^-19*(2.28*10^-25))))/(3.204*10^-19*0.352)= 161.048 mm



forRa+
R5 = ((?(2*2258*1.602*10^-19*(3.75*10^-25))))/(1.602*10^-19*0.352)= 292.091 mm



for Ra2+
R6 = ((?(2*2258*3.204*10^-19*(3.75*10^-25))))/(3.204*10^-19*0.352)= 206.539 mm


for Ra3+
R7 = ((?(2*2258*4.806*10^-19*(3.75*10^-25))))/(4.806*10^-19*0.352)= 168.639 mm


path A = Ca2+ = 87.041 mm

path B = Ca+ = 123.094 mm

path C = Ba2+ = 161.048 mm

path D = Ra3+ = 168.639 mm

path E = Ra2+ = 206.539 mm

path F = Ba+ = 227.756 mm

path G = Ra+ = 292.091 mm

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