calculate the wavelength of an electron m=9.11 x 10^-28 g moving at 3.66x10^6 m/s
To calculate the wavelength of an electron, we can use the de Broglie equation, which states that the wavelength (λ) of a particle is inversely proportional to its momentum (p). The equation is as follows:
λ = h / p
Where:
λ is the wavelength of the particle,
h is the Planck's constant (6.626 x 10^-34 joule-seconds),
p is the momentum of the particle.
To find the momentum (p) of the electron, we can use the equation:
p = m * v
Where:
m is the mass of the electron,
v is the velocity of the electron.
Given:
m = 9.11 x 10^-28 g (mass of the electron)
v = 3.66 x 10^6 m/s (velocity of the electron)
First, let's convert the mass from grams to kilograms by dividing it by 1000:
m = 9.11 x 10^-28 g / 1000 = 9.11 x 10^-31 kg
Now, we can calculate the momentum (p) of the electron using the mass and velocity:
p = m * v
p = 9.11 x 10^-31 kg * 3.66 x 10^6 m/s
p ≈ 3.33 x 10^-24 kg·m/s
Finally, we can calculate the wavelength (λ) using the de Broglie equation:
λ = h / p
λ = 6.626 x 10^-34 J·s / (3.33 x 10^-24 kg·m/s)
λ ≈ 1.987 x 10^-10 m
Therefore, the wavelength of the electron is approximately 1.987 x 10^-10 meters.