calculate the wavelength of an electron m=9.11 x 10^-28 g moving at 3.66x10^6 m/s
The de Broglie wavelength.
wavelength = h/mv
Remember m must be in kg.
To calculate the wavelength of an electron, we can use the de Broglie wavelength equation, which relates the wavelength (λ) of a moving particle to its mass (m) and velocity (v):
λ = h / (m * v)
Where:
λ is the wavelength,
h is the Planck's constant (6.626 x 10^-34 J·s),
m is the mass of the electron, and
v is the velocity of the electron.
First, let's convert the mass of the electron from grams to kilograms:
m = 9.11 x 10^-28 g = 9.11 x 10^-31 kg
Now we can plug the values into the equation:
λ = (6.626 x 10^-34 J·s) / (9.11 x 10^-31 kg * 3.66 x 10^6 m/s)
Simplifying the numerator and denominator:
λ = (6.626 x 10^-34) / (9.11 x 10^-31 kg * 3.66 x 10^6)
λ = 6.626 x 10^-34 / (3.34 x 10^-24 kg·m/s)
Dividing the numerator and denominator by 10^-24:
λ = (6.626 x 10^-34) / (3.34 x 10^0 kg·m/s)
λ = (6.626 x 10^-34) / 3.34
Calculating the numerator:
λ ≈ 1.98 x 10^-34
The wavelength of the electron is approximately 1.98 x 10^-34 meters.
To calculate the wavelength of an electron, we can use the de Broglie wavelength equation, which relates the wavelength (λ) to the momentum (p) of a particle:
λ = h / p
where λ is the wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the electron.
To find the momentum of the electron, we can use the equation:
p = m * v
where p is the momentum, m is the mass of the electron, and v is its velocity.
Given:
Mass of electron, m = 9.11 x 10^-28 g
Velocity of electron, v = 3.66 x 10^6 m/s
First, we need to convert the mass from grams to kilograms. 1 g = 0.001 kg, so the mass becomes:
m = 9.11 x 10^-28 g * 0.001 kg/g = 9.11 x 10^-31 kg
Now, we can calculate the momentum:
p = m * v
p = 9.11 x 10^-31 kg * 3.66 x 10^6 m/s
Multiplying these values, we get:
p ≈ 3.34 x 10^-24 kg·m/s
Finally, we can substitute the values of p and h into the de Broglie wavelength equation to find the wavelength:
λ = h / p
λ = 6.626 x 10^-34 J·s / 3.34 x 10^-24 kg·m/s
Dividing these values, we get:
λ ≈ 1.98 x 10^-10 meters
Therefore, the wavelength of the electron is approximately 1.98 x 10^-10 meters.