Determination of em value of electron.pptx

Determination of e/m value of electron

1. PRESENTATION Determination of e/m value of electron

2. The currently accepted value for e/m is 1.75* 10^11 C/kg. Where m is the mass of electron and e is the charge on it.

3. Historical Review In 1897, the physicist J.J.Thomson set out to prove that the cathode rays originating from a heated cathode were actually a stream of small negatively charged particles, now known as electrons. By studying the centripetal acceleration of electrons in a magnetic field, Thomson was able to successfully determine their charge-to-mass ratio. Thomson's work provided the first empirical evidence that atoms are not themselves fundamental building blocks of matter, paving the way for the field of subatomic physics.

4. Background The mass m is hard to measure experimentally. It is easier to determine the charge-to-mass ratio e/m, from which the mass m can be calculated if the elementary charge e is known. The e/m ratio can be determined experimentally by measuring the trajectory of electrons in an applied magnetic field. Here a question arises: Question; What is the force on an electron in a magnetic field? Which path will the electrons follow in the field?

5. Answer For electrons charge e, moving at speed v in a magnetic field B, the force due to the magnetic field is: F= evB Using Fleming’s left-hand-rule, remember that the force is always perpendicular to both the magnetic field and velocity. Therefore the particles will move in a circle.

6. An introduction to determination of e/m In this experiment you will measure the ratio of charge of an electron to the mass of electron. When an electron enters a region in which there is a uniform magnetic field B, the electron experiences a force F, with the magnitude g iven below: F=evB→(A) This force is perpendicular to v and B and will cause the electron to move in a circular orbit.

7. Equating this force to the mass times the centripetal acceleration, we have the equation below: evB= mv^2/r→(B) Solving the eq.B for e/m we get; e/m=v/Br→© Now the velocity of the electron can be determined from the conservation of energy; 1/2mv^2= eVacc v^2= 2eVacc/m v=√(2eVacc/m)→(D)

8. Final expression Substituting the value of v from the equation (D) in equation © we get the value of e/m for an electron: e/m= 2Vacc/B^2r^2

9. Apparatus An electron gun 2 Helmholtz's coils A spherical shaped glass container Power supply

10. The electron gun The electron gun is mounted within the electron tube with its centerline coincident with the vertical axis of tube. The electron gun has three elements: 1- an indirectly heated cathode 2-a grid 3-a circular disk

11. The Helmholtz Coil The magnetic field is provided by a pair of identical circular coils arranged so that the distance between the coils is equal to the radius of the coils. Such an arrangement, called as Helmholtz coil, provides a highly uniform magnetic field in the region at and near the center of the coil pair. The magnetic field produced by the Helmholtz coil is proportional to the electric current ( I )in the coils. B= jI