To calculate the wavelength associated with a moving particle, we can use the de Broglie wavelength equation, which relates the wavelength (λ) to the momentum (p) of the particle:
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 (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
Given: Mass of the electron (m) = 0.1 x 10^-28 kg Velocity of the electron (v) = 2 x 10^6 m/s
First, we calculate the momentum of the electron:
p = m * v p = (0.1 x 10^-28 kg) * (2 x 10^6 m/s) p = 2 x 10^-22 kg·m/s
Now, we can calculate the wavelength associated with the electron:
λ = h / p λ = (6.626 x 10^-34 J·s) / (2 x 10^-22 kg·m/s) λ = 3.313 x 10^-12 m
Therefore, the wavelength associated with an electron of mass 0.1 x 10^-28 kg moving with a velocity of 2 x 10^6 m/s is approximately 3.313 x 10^-12 meters.