The body perceives calcium (needed for bone growth) and the radioactive element

Question

The body perceives calcium (needed for bone growth) and the radioactive element radium similarly, and so stores both in the bone marrow. Once in the bone marrow, the radium hits nearby bone cells with alpha particles, which cause the cells to deteriorate. To determine radium poisoning, investigators try to identify the various radium isotopes found in bone samples using a mass spectrometer. The figure on the right shows the schematic of a mass spectrometer. The various particles of calcium, barium (another similar element), and radium are injected into a region that has a constant magnetic field. The magnetic field in the figure has a strength of 0.352 T and points out of the screen. To inject the positively-charged isotopes into the magnetic field, they first move through a potential difference of 3082 V between the two plates as shown. ?Using the data shown in the table below, calculate the path radius of the Ca ion.

and . The body perceives calcium (needed for bone growth) the radioactive element radium similarly, and so stores both in the bone marrow. Once in the bone marrow, the radium + hits nearby bone cells with alpha particles, which cause the cells to deteriorate onized To determine radium poisoning, investigators try to identify the various radium isotopes found in bone samples using a mass spectrometer. The figure on the right shows the schematic of a mass spectrometer. The various particles of calcium, barium (another similar element), and radium are+ injected into a region that has a constant magnetic field The magnetic field in the figure has a strength of 0.352 T and points out of the screen. To inject the positively charged isotopes into the magnetic field, they first move through a potential difference of 3082 V between the two plates as shown AV Using the data shown in the table below, calculate the path radius of the Ca ion Number (Scroll down for table and more questions) IIn Using the same data table, match the particles to their path label

Explanation / Answer

Using conservation of energy

Kinetic energy gained = electric potential energy

(0.5) m v2 = q V

v = sqrt(2qV/m)

For Ca+

v = sqrt(2qV/m) = sqrt (2 x 1.602 x 10-19 x 3082/(0.666 x 10-25))

v = 1.22 x 105 m/s

Using the formula

r = mv/qB = (0.666 x 10-25 x 1.22 x 105 /(1.602 x 10-19 x 0.352) ) = 0.144 m

For Ca2+

v = sqrt(2qV/m) = sqrt (2 x 3.204 x 10-19 x 3082/(0.666 x 10-25))

v = 1.72 x 105 m/s

Using the formula

r = mv/qB = (0.666 x 10-25 x 1.72 x 105 /(3.204 x 10-19 x 0.352) ) = 0.102 m

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