What is the de Broglie wavelength of a 5.0-eV electron?
E=5eV=8•10⁻¹⁹ J
λ=h/p = h/sqrt(2mE) =
=6.63•10⁻³⁴/sqrt(2•9.1•10⁻³¹•8•10⁻¹⁹)=5.5•10⁻¹⁰ m
To find the de Broglie wavelength of an electron, you can use the de Broglie wavelength formula:
λ = h / p
Where:
λ is the de Broglie wavelength (in meters),
h is the Planck's constant (6.626 x 10^-34 J·s),
p is the momentum of the electron (in kg·m/s).
The momentum of an electron can be calculated using the formula:
p = √(2mE)
Where:
m is the mass of an electron (9.10938356 x 10^-31 kg),
E is the energy of the electron (in joules).
Given that the energy of the electron is 5.0 eV, we need to convert it to joules.
1 eV = 1.602176634 x 10^-19 J
Converting the energy to joules:
E = 5.0 eV * 1.602176634 x 10^-19 J/eV
After this conversion, we can calculate the momentum of the electron using the above formula. Once we have the momentum, we can substitute it into the de Broglie wavelength formula to find the de Broglie wavelength.
To find the de Broglie wavelength of an electron, we can use the de Broglie equation:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck's constant (approximately 6.626 x 10^-34 J·s), and p is the momentum of the electron.
To find the momentum of an electron, we can use the equation:
p = √(2mE)
where p is the momentum, m is the mass of the electron (approximately 9.10938356 × 10^-31 kg), and E is the energy of the electron.
Given that the energy of the electron is 5.0 eV, we need to convert it to joules. The conversion is 1 eV = 1.602 x 10^-19 J.
So, 5.0 eV can be converted to 5.0 x 1.602 x 10^-19 J = 8.01 x 10^-19 J.
Now we can plug in the values into the equation for momentum:
p = √(2mE) = √(2 x 9.10938356 × 10^-31 kg x 8.01 x 10^-19 J)
Calculating this expression will give us the momentum in kg·m/s.
Finally, we can use the momentum value to calculate the de Broglie wavelength using the equation:
λ = h / p
Plug in the calculated value of momentum and the value of Planck's constant to find the de Broglie wavelength.