Please show all steps thank you Elements that appear in the

Please show all steps, thank you!

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 potential difference of 2464 V on the two plates shown. Using the data shown in the table below, calculate the path radius of the Ca+ ion.

Solution

For circular motion,

the magnetic force must provide the necessary centripetal force

So, qvB = mv^2/r

So, r = mv/qB

here m = mass of Ca+ ion = 40.08*10^-3/(6.022*10^23) = 6.66*10^-26 kg

q = 1.6*10^-19 C

B = 0.452 T

Now, for a voltage of V = 2464 V, the kinetic energy of the ion,

0.5*mv^2 = V*q

So, v = sqrt(2Vq/m)

So, r = m*sqrt(2*Vq/m)/qB

So, r = 6.66*10^-26*sqrt(2*2464*1.6*10^-19/(6.66*10^-26))/(1.6*10^-19*0.452)

So, r = 0.1 m <-------answer