Calculate the velocities of electrons with de Broglie wavelengths of 1.7 102 nm and 5.0 nm, respectively.
To calculate the velocities of electrons with de Broglie wavelengths, we can use the de Broglie wavelength equation, which is given by:
λ = h / (m*v)
Where:
λ is the de Broglie wavelength
h is the Planck's constant (6.626 × 10^(-34) J·s)
m is the mass of the electron (9.10938356 × 10^(-31) kg)
v is the velocity of the electron
Let's calculate the velocities for the given de Broglie wavelengths:
For the de Broglie wavelength of 1.7 × 10^2 nm:
First, convert the wavelength to meters by dividing by 10^9:
λ = 1.7 × 10^2 nm / 10^9 = 1.7 × 10^(-7) m
Substitute the values into the de Broglie equation and solve for v:
1.7 × 10^(-7) = (6.626 × 10^(-34)) / ((9.10938356 × 10^(-31)) * v)
Rearrange the equation to solve for v:
v = (6.626 × 10^(-34)) / ((9.10938356 × 10^(-31)) * (1.7 × 10^(-7)))
Calculate the result using a calculator:
v ≈ 2.94 × 10^6 m/s
So, the velocity of the electron with a de Broglie wavelength of 1.7 × 10^2 nm is approximately 2.94 × 10^6 m/s.
Now, let's calculate the velocity for the de Broglie wavelength of 5.0 nm:
Convert the wavelength to meters:
λ = 5.0 nm / 10^9 = 5.0 × 10^(-9) m
Substitute the values into the de Broglie equation and solve for v:
5.0 × 10^(-9) = (6.626 × 10^(-34)) / ((9.10938356 × 10^(-31)) * v)
Rearrange the equation to solve for v:
v = (6.626 × 10^(-34)) / ((9.10938356 × 10^(-31)) * (5.0 × 10^(-9)))
Calculate the result:
v ≈ 1.453 × 10^6 m/s
So, the velocity of the electron with a de Broglie wavelength of 5.0 nm is approximately 1.453 × 10^6 m/s.