ements that appear in the same column of the periodic table often share similar

Question

ements 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." ionized isotope 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 2773 V on the two plates shown +-AV- detectorE Using the data shown in the table below, calculate the path radius of the Cat ion Number (Scroll down for table and more questions) Using the same data table, match the particles to their path label.

Explanation / Answer

First equation:
1.) F=ma
2.) a=m*(v^2/r)

Substitute 2 into 1.   F=m*(v^2/r)
The force of a charge particle = F=qVB => call this equation 3 and substitute into equation 1.
qvB=m*(v^2/r) v's on both sides, and cancels out.
qB=m*(v/r)
We need to find v, so how do we find v?

A voltage was applied which accelerated the Ca ion. The voltage*charge of the ion gives us the potential energy lost and the amount of KE of the Ca ion. So, PE=q*V and KE=1/2mv^2, equate to each other and solve for v:

qV=1/2mv^2
sqrt*[2*qV/m]=v <= call this equation 4 and substitute it into are already substituted equation 1.
qB=m*(sqrt*[2*qV/m]/r)
r=sqrt[2*qV/m]/(qB/m)
Where q=1.602 × 10^-19 C,   V=2773 V, m=40.1amu*(1.661 × 10^-27 kg/1 amu)=6.661 x 10^-26 kg, B=0.452 T
Then
r=sqrt[2*1.602 × 10^-19 C*2773 V/6.661 x 10^-26 kg]/(1.602 × 10^-19 C*0.452 T/6.661 x 10^-26 kg )
r=0.106 m

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