the de broglie wavelength of an electron with a velocity of 6.00 x 10^6 m/s is ____m. the mass of the electron is 9.11 x 10^-28g.
To find the de Broglie wavelength of an electron, you can use the de Broglie wavelength equation:
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 particle.
First, we need to find the momentum of the electron. The momentum (p) is given by the equation:
p = mv
where m is the mass of the electron and v is the velocity.
Given data:
Mass of the electron (m) = 9.11 x 10^(-31) kg (convert the given value from grams to kilograms)
Velocity (v) = 6.00 x 10^6 m/s
First, convert the mass from grams to kilograms:
9.11 x 10^(-28) g = 9.11 x 10^(-31) kg
Now, calculate the momentum (p) using the given mass and velocity:
p = (9.11 x 10^(-31) kg) * (6.00 x 10^6 m/s)
Next, substitute the calculated value of the momentum (p) into the de Broglie wavelength equation:
λ = (h) / (p)
Substitute the known values:
λ = (6.626 x 10^(-34) J·s) / (calculated value of p)
Now, solve for the wavelength (λ).
To calculate the de Broglie wavelength (λ) of an electron, you can use the equation:
λ = h / (m * v)
Where:
- λ is the de Broglie wavelength
- h is the Planck's constant (6.626 x 10^-34 J∙s)
- m is the mass of the electron
- v is the velocity of the electron
Let's substitute the given values into the equation:
m = 9.11 x 10^-28 g = 9.11 x 10^-31 kg (since 1 kg = 1000 g)
v = 6.00 x 10^6 m/s
Now, we can calculate:
λ = (6.626 x 10^-34 J∙s) / (9.11 x 10^-31 kg * 6.00 x 10^6 m/s)
1. Calculate the denominator first:
(9.11 x 10^-31 kg * 6.00 x 10^6 m/s) = 5.466 x 10^-24 kg·m/s
2. Now divide the numerator by the denominator:
(6.626 x 10^-34 J∙s) / (5.466 x 10^-24 kg·m/s) = 1.212 x 10^-10 m
Therefore, the de Broglie wavelength of the electron is 1.212 x 10^-10 meters.
w = wavelength.
w = h/mv
Substitute h and v from the problem. Convert m to kg.