Charge to mass ratio of electron
Charge to mass ratio of electron
A magnetic field produced by Helmholz coils is used to deflect electrons into circular paths whose radii are known. By knowing the energy of the electrons and the magnetic field strength, the ratio of the charge to mass (e/m) of the electron is determined.
Thomson was able to determine the charge-to-mass ratio of the electron,
The charge-to-mass ratio of an electron is 1.76 x1011coulomb/kg
Electrons are thermally emitted from a surface and accelerated through a potential difference V. The kinetic energy of the accelerated electrons equals the energy they gain as a result of being accelerated through the potential difference. In other words:
½ m v2 = eV
and solving for velocity,
v = (2eV/m)1/2 .
In this equation m is the mass of the electron and e is the charge of the electron.
The beam of electrons enters the region where a magnetic field B is set up by the Helmholz coils. The beam is deflected into a circular path of radius R by the magnetic force and undergoes a centripetal acceleration. This can be expressed as
evB = mv2/r
When the velocity is eliminated between the above two equations, then the charge to mass ratio can be written as
e/m = 2V/(B2r2)
The magnetic field due to the Helmholz coils can be expressed as B = 8moNI/(125)1/2a
where N is the number of turns of wire on each coil, I is the current through the coils, a is the mean radius of the coils, and mo is the permeability of free space. (mo = 4p x 10-7 Tm/A)
While carrying out discharge tube experiment, Thomson observed that the particles of the cathode deviate from their path. He noticed the amount of deviation in the presence of electrical or magnetic field depends on various related parameters. They are:
- Particles with a greater magnitude of the charge experienced greater interaction with the electric or magnetic field. Thus, they exhibited a greater deflection.
- Lighter particle experienced greater deflection. Thus, deflection is inversely proportional to the mass of the particle.
- Deflection of the particle from their path is directly proportional to the strength of the electrical and the magnetic field present.
experimental observations.
- The electrons deviated from their path and hit the cathode ray tube at point ‘x’ in the presence of a lone electric field.
- Similarly, electron strikes the discharge tube at point ‘z’ when only the magnetic field was present.
- Thus, to make electrons continue on the same path we need to balance the electric and magnetic field acting on them.
- Finally, based on the deflection of the electron, Thomson calculated the value of charge to mass ratio of the electron.
Charge to mass ratio of electron The charge to mass ratio of the electron is given by :
e/m = 1.76 × 1011 C/kg
Where,
m = mass of an electron in kg = 9.10938356 × 10-31 kilograms.
e = magnitude of the charge of an electron in coulombs = 1.602 x 10-19 coulombs.
Thomson was able to determine the charge-to-mass ratio of the electron,
The charge-to-mass ratio of an electron is 1.76 x1011coulomb/kg
Electrons are thermally emitted from a surface and accelerated through a potential difference V. The kinetic energy of the accelerated electrons equals the energy they gain as a result of being accelerated through the potential difference. In other words:
½ m v2 = eV
and solving for velocity,
v = (2eV/m)1/2 .
In this equation m is the mass of the electron and e is the charge of the electron.
The beam of electrons enters the region where a magnetic field B is set up by the Helmholz coils. The beam is deflected into a circular path of radius R by the magnetic force and undergoes a centripetal acceleration. This can be expressed as
evB = mv2/r
When the velocity is eliminated between the above two equations, then the charge to mass ratio can be written as
e/m = 2V/(B2r2)
The magnetic field due to the Helmholz coils can be expressed asB = 8moNI/(125)1/2a
where N is the number of turns of wire on each coil, I is the current through the coils, a is the mean radius of the coils, and mo is the permeability of free space. (mo = 4p x 10-7 Tm/A)
While carrying out discharge tube experiment, Thomson observed that the particles of the cathode deviate from their path. He noticed the amount of deviation in the presence of electrical or magnetic field depends on various related parameters. They are:
- Particles with a greater magnitude of the charge experienced greater interaction with the electric or magnetic field. Thus, they exhibited a greater deflection.
- Lighter particle experienced greater deflection. Thus, deflection is inversely proportional to the mass of the particle.
- Deflection of the particle from their path is directly proportional to the strength of the electrical and the magnetic field present.
experimental observations.
- The electrons deviated from their path and hit the cathode ray tube at point ‘x’ in the presence of a lone electric field.
- Similarly, electron strikes the discharge tube at point ‘z’ when only the magnetic field was present.
- Thus, to make electrons continue on the same path we need to balance the electric and magnetic field acting on them.
- Finally, based on the deflection of the electron, Thomson calculated the value of charge to mass ratio of the electron.
The charge to mass ratio of the electron is given by :
e/m = 1.76 × 1011 C/kg
Where,
m = mass of an electron in kg = 9.10938356 × 10-31 kilograms.
e = magnitude of the charge of an electron in coulombs = 1.602 x 10-19 coulombs.
