What is the de Broglie wavelength of an electron that strikes the back of the face of a TV screen at 1/9 the speed of light?
To calculate the de Broglie wavelength of an electron, we can use the formula:
λ = h / p,
where λ is the de Broglie wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the particle.
To find the momentum of the electron, we can use the formula:
p = m * v,
where p is the momentum, m is the mass of the electron (9.10938356 × 10^-31 kg), and v is the velocity of the electron.
Given that the electron strikes the back of the face of a TV screen at 1/9 the speed of light, we need to calculate the velocity of the electron first:
v = (1/9) * c,
where v is the velocity and c is the speed of light (approximately 3 x 10^8 m/s).
Now we can substitute the velocity back into the momentum formula:
p = (9.10938356 × 10^-31 kg) * [(1/9) * (3 x 10^8 m/s)].
Once we have the momentum, we can calculate the de Broglie wavelength by substituting the values into the formula:
λ = (6.626 x 10^-34 J·s) / p.
Finally, we can plug in the values into the equation to calculate the de Broglie wavelength.
Calculate the momentum p of the electron using the classical formula,
p = m v = m c/9
m is the electron mass.
(It is OK to use the classical formula for momentum since the speed is much less than c. The correction factor is sqrt {1/[1 - (v/c)^2]} is close to 1)
For the de Broglie wavelength L, use
L = h/p