To determine the wavelength of a photon that would have the same momentum as an electron moving at a given velocity, we can use the de Broglie wavelength equation:
λ = h / p
Where: λ = wavelength h = Planck's constant (approximately 6.626 x 10^-34 J·s) p = momentum
The momentum (p) of an object is calculated as the product of its mass (m) and velocity (v):
p = m * v
For an electron, the mass (m) is approximately 9.11 x 10^-31 kg. Given that the electron is moving at a velocity of 3.50 x 10^6 m/s, we can calculate its momentum:
p = (9.11 x 10^-31 kg) * (3.50 x 10^6 m/s)
Simplifying:
p = 3.19 x 10^-24 kg·m/s
Now, we can substitute the calculated momentum (p) into the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J·s) / (3.19 x 10^-24 kg·m/s)
Simplifying:
λ ≈ 2.07 x 10^-10 meters
Therefore, a photon with a wavelength of approximately 2.07 x 10^-10 meters would have the same momentum as an electron moving at 3.50 x 10^6 m/s.