Find e/m for electrons in an experiment in which H=2.68 gauss, S=5.00 cm, E=6.3x10^10 volts/cm, and 0=0.100 radian.
the 0 in 0=0.100 is a zero with a line through it
To find the value of e/m for electrons in the given experiment, we need to use the equation for the deflection of charged particles in a magnetic field.
The equation is given as: r = (e/m) * (S/V) * H^2 * sin(θ)
Where:
- r is the radius of the circular path of the electron
- e/m is the charge-to-mass ratio of the electron (what we need to find)
- S is the distance between the electrodes
- V is the accelerating voltage
- H is the magnetic field strength
- θ is the angle of deflection
In the given question, it seems that the variables are as follows:
H = 2.68 gauss (magnetic field strength)
S = 5.00 cm (distance between the electrodes)
E = 6.3x10^10 volts/cm (accelerating voltage)
θ = 0.100 radians (angle of deflection)
First, let's convert the magnetic field strength from gauss to teslas:
1 gauss = 1x10^-4 tesla
Therefore, H = 2.68 gauss * 1x10^-4 tesla/gauss = 2.68x10^-4 tesla
Next, let's convert the angle of deflection from radians to degrees:
1 radian ≈ 57.2958 degrees
Therefore, θ = 0.1 radians * 57.2958 degrees/radian ≈ 5.73 degrees
Now we can substitute the given values into the equation:
r = (e/m) * (S/V) * H^2 * sin(θ)
For simplicity, let's assume that V is 1 volt/cm.
r = (e/m) * (5.00 cm / 1 volt/cm) * (2.68x10^-4 tesla)^2 * sin(5.73 degrees)
r = (e/m) * 5.00 * (2.68x10^-4)^2 * sin(5.73 degrees)
Now we can rearrange the equation to solve for e/m:
(e/m) = r / (5.00 * (2.68x10^-4)^2 * sin(5.73 degrees))
Plug in the value of r (the radius of the circular path of the electron) that you have measured in your experiment. Substitute the other values.
By calculating this expression, you will find the e/m value for electrons in the given experiment.