An electron strikes the back of a TV screen at 1/10 the speed of light.
What is the speed of the electron?
What is the momentum of the electron?
What is the deBrogile wavelength of the electron?
v = 0.1 c = ?
momentum = m*v = ?
de Broglie wavelength = h/{momentum) = ?
You do the numbers. You will need to look up the speed of light (c), electrom mass (m), and Planck's constant (h).
I am using nonrelativistic (before Einstein) formulas. The correct formulas will differ by a factor of sqrt [1 - (v/c)^2]= 0.995
Consider the de Broglie wavelength of an electron that strikes the back face of one of the early models of a TV screen at 1/10 the speed of light
To begin, we can use the given information to find the speed of the electron. The speed of light is approximately 3 x 10^8 meters per second.
1. Speed of the electron:
Given that the electron strikes the back of the TV screen at 1/10 the speed of light, we can calculate its speed by multiplying the speed of light by 1/10:
Speed of the electron = (1/10) x (3 x 10^8)
Speed of the electron = 3 x 10^7 meters per second
Next, we can determine the momentum of the electron using its mass and velocity. The mass of an electron is approximately 9.1 x 10^-31 kilograms.
2. Momentum of the electron:
Momentum is calculated by multiplying the mass (m) of an object by its velocity (v):
Momentum = mass x velocity
Momentum = 9.1 x 10^-31 x 3 x 10^7
Momentum = 2.73 x 10^-23 kilograms meters per second
Lastly, we can calculate the de Broglie wavelength of the electron using the de Broglie wavelength formula. The formula is given by λ = h / p, where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.
3. de Broglie wavelength of the electron:
Using the given value of Planck's constant (h ≈ 6.626 x 10^-34 J·s) and the momentum calculated previously, we can substitute the values into the formula, λ = h / p:
de Broglie wavelength = 6.626 x 10^-34 / (2.73 x 10^-23)
de Broglie wavelength ≈ 2.43 x 10^-11 meters
So, the speed of the electron is approximately 3 x 10^7 meters per second, the momentum of the electron is approximately 2.73 x 10^-23 kilograms meters per second, and the de Broglie wavelength of the electron is approximately 2.43 x 10^-11 meters.