Question

6) A solution of sodium chloride (molecular weight 58.5) is electrolyzed and it is found that a
current of 1 A liberates 1.3 x 10-3 kg of chlorine (atomic weight 35.5) in one hour. Sodium
chloride crystals of density 2.17 x 103 kg/m3 are analyzed by x rays and the unit cell parameter is
found to be 5.6 x 10-10 m. From these data calculate the charge on a monovalent ion.

7) In a Milikan oil-drop experiment, a certain droplet was found to fall freely in air at a steady rate
of 1.15 x 10-4 m/sec. between horizontal plates 3 mm apart. When an electrical potential
difference of 400 V was applied between the plates, the droplet rose steadily at 1.2 x 10-5 m/sec;
while at 300 V, the droplet fell steadily at 1.8 x 10-5 m/sec. Find the magnitude of the charge on
the drop, given that the viscosity of the air is 1.8 x 10-5 mks units, and the density of the oil used
was 900 kg/m3.

8) In an experiment to determine e/m for electrons by J. J. Thomson’s method, the particles were
deflected by a uniform electrostatic field of 50000 V/m applied between plates 0.05 m long. The
deflection produced on a screen placed 0.3 m away from the center of the plates was 0.05 m.
This deflection was exactly canceled by applying a magnetic field of 0.001 Tesla coextensive with
the electric field. Find the speed of the electrons, their specific charge, and the accelerating
voltage.

Answer 1

6) Total charge liberated in a given time is,

the total mass of Chlorine liberated

mass of single Chlorine atom

So, the total number of Chlorine ions liberated,

So, charge on a single Chlorine ion is,

7) in the first case, the gravitational force is balanced by the viscous force; hence the velocity remains steady

according to Stokes's law,

but mass

rearranging,

this is a radius of the oil drop.

Now, in the next case, the electric force of repulsion is added to the viscous force.

but

Solving for q, we get,

  

  

this is a charge on the oil drop.

8) when electric force is balanced by magnetic force,

time to reach the screen,

acceleration due to the electric force is

displacement due to this acceleration is

(this answer is about 3 times less than the expected value - might be due to relativistic effects or check the calculations again,

the theoretical value of the specific charge is )

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