What must be the velocity of a beam of electron if they are to display a de broglie wavelength of 1A°?
wavelength = h/mv
Convert 1A to m.
To determine the velocity of a beam of electrons required to display a de Broglie wavelength of 1 Å (Angstrom), we can use the de Broglie wavelength formula:
λ = h / p
Where:
λ is the de Broglie wavelength,
h is the Planck's constant (h ≈ 6.626 x 10^-34 J·s),
p is the momentum of the electron.
We can rearrange the formula to solve for the momentum:
p = h / λ
The momentum of an electron can be calculated using the formula:
p = m * v
Where:
m is the mass of the electron (m ≈ 9.109 x 10^-31 kg),
v is the velocity of the electron.
Now, substitute the expression for the momentum in terms of velocity into the de Broglie wavelength formula:
h / λ = m * v
Solving for v, the velocity of the electron, we get:
v = h / (m * λ)
Substituting the given values into the equation:
v = (6.626 x 10^-34 J·s) / (9.109 x 10^-31 kg * 1 x 10^-10 m)
Calculating the expression:
v ≈ 727,414 m/s
Therefore, the velocity of the beam of electrons should be approximately 727,414 meters per second (m/s) in order to display a de Broglie wavelength of 1 Å.