What is the wavelength of an electron moving at 2.60% of the speed of light?
1 m
v = 0.026•c
β = v/c = 0.026.
h = 6.63•10^-34 J•s
Relativistic momentum
p = mv/sqrt(1-β²) =
= 9.1•10^-31•0.026• 3•10^8 / sqrt(1 - 0.026²)=7.1•10^-24 kg•m/s.
de Broglie wavelength
λ = h/p = 6.63•10^-34/7.1•10^-24 =
=9.33•10^-11 m
To calculate the wavelength of an electron moving at a given speed, we can use the de Broglie wavelength equation:
λ = h / p
Where:
λ is the wavelength
h is the Planck's constant (approximately 6.626 x 10^-34 J·s)
p is the momentum of the electron, which can be calculated as the product of the mass (m) and velocity (v) of the electron.
First, let's calculate the momentum of the electron:
p = m * v
Given that the electron is moving at 2.60% of the speed of light and the speed of light is approximately 3 x 10^8 m/s, we can calculate the actual velocity (v) of the electron as follows:
v = 0.026 * 3 x 10^8 m/s
Now, using the mass of an electron (me) as approximately 9.11 x 10^-31 kg, we can substitute the values into the momentum equation:
p = (9.11 x 10^-31 kg) * (0.026 * 3 x 10^8 m/s)
Once we have the momentum value (p), we can substitute it into the de Broglie wavelength equation to get the wavelength (λ):
λ = (6.626 x 10^-34 J·s) / p
After performing the calculations, we can determine the wavelength. Please note that you have provided the unit as "1 m." If you meant to ask for the numerical value of the wavelength, please clarify the desired unit or let me know if you meant something else.
To determine the wavelength of an electron moving at a certain percentage of the speed of light, we can use the de Broglie wavelength equation:
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.
The mass of an electron is approximately 9.10938356 x 10^-31 kg.
First, we need to calculate the velocity of the electron. We know that the electron is moving at 2.60% of the speed of light, which is:
v = 2.60% * c
where c is the speed of light (approximately 3.00 x 10^8 m/s).
v = 0.026 * 3.00 x 10^8 m/s
Now, we can calculate the wavelength using the de Broglie equation:
λ = (6.626 x 10^-34) / (9.10938356 x 10^-31 * [0.026 * 3.00 x 10^8])
Calculating this expression will give us the wavelength of the electron.