what is the characteristic wavelength of an electron (in nm) that has a velocity of 5.97 X 10^6 ms^-1 (me=9.11 X 10^-31kg)?
To find the characteristic wavelength of an electron, we can use the de Broglie wavelength equation, which relates the wavelength of a particle to its momentum.
The de Broglie wavelength equation is as follows:
λ = h / p
Where:
λ is the wavelength of the particle
h is the Planck's constant (h = 6.626 x 10^-34 Js)
p is the momentum of the particle
To find the momentum of an electron, we can use the definition of momentum:
p = m * v
Where:
p is the momentum
m is the mass of the electron (me = 9.11 x 10^-31 kg)
v is the velocity of the electron (5.97 x 10^6 m/s, given in the question)
Let's calculate the momentum of the electron first:
p = m * v
p = (9.11 x 10^-31 kg) * (5.97 x 10^6 m/s)
Now, let's plug the calculated momentum into the de Broglie wavelength equation to find the characteristic wavelength of the electron:
λ = h / p
λ = (6.626 x 10^-34 Js) / (9.11 x 10^-31 kg * 5.97 x 10^6 m/s)
Now, divide the Planck's constant by the calculated momentum to find the characteristic wavelength.
Finally, convert the characteristic wavelength from meters to nanometers by multiplying it by 10^9 since 1 meter is equal to 10^9 nanometers.
Remember to perform the calculations using the given values and units to obtain the final answer.
what is the charactristic wavelength of an electron (in nm) that has a velocity of 5.97×10 m(Me=9.11×10
De Broglie wavelength
wavelength = Planck's constant / momentum = h / (m v)