To calculate the wavelength associated with an electron traveling at 40% of the velocity of light, we can use the de Broglie wavelength equation, which relates the wavelength (λ) of a particle to its momentum (p):
λ = h / p
where λ is the wavelength, h is the Planck's constant (approximately 6.626 x 10^-34 J·s), and p is the momentum of the particle.
The momentum of a particle can be calculated using its mass (m) and velocity (v) through the equation:
p = m * v
Given: Mass of the electron (m) = 9.11 x 10^-28 g = 9.11 x 10^-31 kg Velocity of the electron (v) = 0.4 * c (c is the speed of light, approximately 3 x 10^8 m/s)
First, let's calculate the momentum of the electron:
p = m * v p = (9.11 x 10^-31 kg) * (0.4 * 3 x 10^8 m/s)
Now, we can calculate the wavelength using the de Broglie wavelength equation:
λ = h / p λ = (6.626 x 10^-34 J·s) / (momentum calculated above)
Performing the calculations will give you the desired wavelength associated with the electron traveling at 40% of the velocity of light.