To determine the kinetic energy (KE) of the electron in electron volts (eV) from the given parameters of the experiment, we can follow a systematic approach. The key points to consider are the voltage difference across the deflecting plates and the radius of the circular path the electron takes due to the electric field created by the plates.
Understanding the Relationship Between Voltage and Kinetic Energy
The kinetic energy of an electron can be derived from the work done on it by the electric field when it is accelerated through a potential difference (V). The formula for kinetic energy (KE) in terms of voltage is:
KE = eV
Here, e is the charge of the electron, approximately equal to 1.6 x 10-19 coulombs, and V is the potential difference in volts. In this case, the voltage difference is given as 40V.
Calculating the Kinetic Energy
Substituting the values into the formula:
KE = e × V = (1.6 x 10-19 C) × (40 V)
Now, let's calculate this:
KE = 1.6 x 10-19 C × 40 V = 6.4 x 10-18 joules
Converting Joules to Electron Volts
Since we want the kinetic energy in electron volts, we can use the conversion factor where 1 eV is equal to 1.6 x 10-19 joules. To convert joules to electron volts, we divide the energy in joules by the charge of the electron:
KE (in eV) = KE (in joules) / e
Substituting the values:
KE (in eV) = (6.4 x 10-18 J) / (1.6 x 10-19 J/eV)
Calculating this gives:
KE (in eV) = 40 eV
Summary of Findings
Thus, the kinetic energy of the electron, after being accelerated through a potential difference of 40V, is:
KE = 40 eV
This result aligns with our expectations, as the kinetic energy gained by the electron is directly proportional to the voltage through which it is accelerated. Therefore, in this experiment, the electron has a kinetic energy of 40 electron volts.
