To determine the value of e/m of an electron . Modern Physics Lab

To determine the value of
𝑒/m (charge-to-mass ratio) of an electron in a modern physics lab, you can use the Thomson method or a variation of it, often involving a cathode ray tube (CRT) and a magnetic field. Here's an outline of a common experimental setup and procedure:

Experimental Setup:
Helmholtz Coils: Two identical coils are placed parallel to each other to produce a uniform magnetic field.
Electron Gun: A cathode emits electrons, which are accelerated through a known potential difference (V).
Magnetic Field (B): A uniform magnetic field is applied perpendicular to the motion of electrons.
Vacuum Tube: The experiment takes place in a vacuum to minimize interactions with air molecules.
Procedure:
Accelerating Electrons: Electrons are accelerated by an electric potential
𝑉
V. The kinetic energy gained by the electron is:

From this, the velocity of the electrons can be expressed as:
V
Applying Magnetic Field: A magnetic field
𝐵
B perpendicular to the electron's path causes the electrons to move in a circular trajectory. The force acting on the electrons due to the magnetic field is:

F=evB
This is the centripetal force that makes the electron follow a circular path:
Combining Equations: Substituting
𝑣
v from the kinetic energy equation:

𝑒
𝑚
=
2
𝑉
𝐵
2
𝑟
2
m
e
​
=
B
2
r
2

2V
​

Measurement:
Measure the radius
𝑟
r of the electron's path, the magnetic field
𝐵
B, and the accelerating voltage
𝑉
V.
Use these values to calculate
𝑒
𝑚
m
e
​
.
Conclusion:
By performing this experiment and substituting your measured values into the formula, you can determine the charge-to-mass ratio of the electron. The accepted value of
𝑒
𝑚
m
e
​
for an electron is approximately
1.76
×
1
0
11
 
C/kg
1.76×10
11
C/kg.