calculate the velocities of electrons with de Broglie wavelengths of 1.0x10^2nm and 1.0nm
velocity= planck's constant/(masselectron*wavelength)
The velocity of an electron with de Broglie wavelength of 1×10
−2
nm is:
To calculate the velocity of an electron with a de Broglie wavelength, we can use the de Broglie equation:
wavelength = h / mv
where:
- wavelength is the de Broglie wavelength (given in nm)
- h is the Planck's constant (6.626 x 10^-34 Js)
- m is the mass of the electron (9.10938356 x 10^-31 kg)
- v is the velocity of the electron
Let's calculate the velocity for the given de Broglie wavelengths:
For the wavelength of 1.0 x 10^2 nm:
wavelength = 1.0 x 10^2 nm = 1.0 x 10^-7 meters
Using the de Broglie equation:
1.0 x 10^-7 = (6.626 x 10^-34) / (9.10938356 x 10^-31 * v)
Rearranging the equation to solve for v:
v = (6.626 x 10^-34) / (9.10938356 x 10^-31 * 1.0 x 10^-7)
Calculating the value of v:
v = 7273.805 m/s
So, the velocity of an electron with a de Broglie wavelength of 1.0 x 10^2 nm is approximately 7273.805 m/s.
Now, let's calculate the velocity for the de Broglie wavelength of 1.0 nm:
Using the same steps as above,
wavelength = 1.0 nm = 1.0 x 10^-9 meters
1.0 x 10^-9 = (6.626 x 10^-34) / (9.10938356 x 10^-31 * v)
Rearranging the equation to solve for v:
v = (6.626 x 10^-34) / (9.10938356 x 10^-31 * 1.0 x 10^-9)
Calculating the value of v:
v = 727382.988 m/s
So, the velocity of an electron with a de Broglie wavelength of 1.0 nm is approximately 727382.988 m/s.