What is the wavelength of an electron traveling at 7.59% of the speed of light?
wavelength = h/mv
h = 6.626E-34 Js
m = 9.109E-31 kg
v = 3E8m/s x 0.0758
To calculate the wavelength of an electron traveling at a certain velocity, we can use the de Broglie wavelength equation:
λ = h / (m * v)
where:
- λ is the wavelength
- h is the Planck's constant (h = 6.626 x 10^-34 J·s)
- m is the mass of the electron (m = 9.10938356 x 10^-31 kg)
- v is the velocity of the electron
Given that the electron is traveling at 7.59% of the speed of light, we can calculate its velocity (v) as follows:
v = 0.0759 * c
where:
- c is the speed of light (c = 3 x 10^8 m/s)
Let's calculate the velocity:
v = 0.0759 * 3 x 10^8 m/s
v ≈ 2.277 x 10^7 m/s
Now, we can substitute the values into the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J·s) / (9.10938356 x 10^-31 kg * 2.277 x 10^7 m/s)
Calculating this, we get:
λ ≈ 2.75 x 10^-10 meters
Therefore, the wavelength of an electron traveling at 7.59% of the speed of light is approximately 2.75 x 10^-10 meters.
To determine the wavelength of an electron traveling at a certain speed, you can use the de Broglie wavelength equation, which relates the wavelength of a particle to its momentum. The equation is given as:
λ = h / p
Where:
λ is the wavelength
h is Planck's constant (approximately equal to 6.626 x 10^-34 J·s)
p is the momentum of the electron, calculated as the product of its mass (m) and velocity (v).
In this case, you are given the velocity of the electron as a percentage of the speed of light. To convert this to the actual velocity (v), multiply the given percentage (7.59%) by the speed of light (c) in meters per second (approximately 3 x 10^8 m/s).
v = 0.0759 * c
Now, you have the velocity of the electron. To find the momentum (p), multiply the mass of the electron (approximately 9.109 x 10^-31 kg) by its velocity (v).
p = m * v
Finally, substitute the calculated momentum into the de Broglie wavelength equation to get the wavelength of the electron:
λ = h / p
Calculate λ using the values obtained, and you will have the answer.