An electron enters the region with u=3*10 6 m/s and E=200N/C. The horizontal length of the plate is 0.1m. Find
a. The wavelength of the electron while it is in the electric field
b. If the electron enters the field at time,t=0.find the time at which it leaves the field
C. If the vertical position of the electron as it enters the field is yi=0, what is the vertical position when it leaves the field
want the answer with its workings
To find the answers to these questions, we can use basic physics principles and equations. Let's go through the steps to find the solutions.
a. The wavelength of the electron while it is in the electric field:
Step 1: Determine the acceleration of the electron in the electric field.
The acceleration of a charged particle in an electric field is given by the equation a = qE/m, where q is the charge of the particle, E is the electric field strength, and m is the mass of the particle. In this case, the charge of an electron is q = -1.6 x 10^-19 C, and the mass of an electron is m = 9.11 x 10^-31 kg. The acceleration is therefore:
a = (qE) / m.
Step 2: Calculate the time spent in the electric field.
Since we know the initial velocity of the electron (u) and the horizontal length of the plate (0.1m), we can calculate the time spent in the electric field using the equation:
t = d / u,
where d is the horizontal length of the plate.
Step 3: Calculate the final velocity of the electron.
The final velocity of the electron can be calculated using the equation:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time spent in the electric field.
Step 4: Calculate the de Broglie wavelength.
The de Broglie wavelength of a particle is given by the equation:
λ = h / p,
where λ is the wavelength, h is Planck's constant (h = 6.626 x 10^-34 J·s), and p is the momentum of the particle. The momentum can be calculated using the equation:
p = m * v,
where m is the mass of the electron and v is its final velocity.
b. If the electron enters the field at time, t = 0, find the time at which it leaves the field:
Since we already know the time spent in the electric field (calculated in step 2), we can add it to the initial time (t = 0) to find the time at which the electron leaves the field.
c. If the vertical position of the electron as it enters the field is yi = 0, what is the vertical position when it leaves the field:
Since the electron only experiences acceleration in the horizontal direction, the vertical position remains unchanged. Therefore, the vertical position when the electron leaves the field will still be yi = 0.