(a) If the wavelength of an electron is 5.37 ✕ 10−7 m, how fast is it moving?
(b) If the electron has a speed equal to 3.80 ✕ 106 m/s, what is its wavelength?
What equation should I use?
wavelength= planck's constant/(mass*velocity)
http://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/02._Fundamental_Concepts_of_Quantum_Mechanics/De_Broglie_Wavelength
To find the velocity of an electron given its wavelength, you can use the de Broglie equation, which relates the wavelength of a particle to its momentum. The de Broglie equation is given by:
λ = h / p
Where:
λ is the wavelength of the particle,
h is the Planck's constant (6.626 x 10^-34 J·s),
p is the momentum of the particle.
(a) To determine how fast the electron is moving, you need to calculate its momentum using the de Broglie equation. Rearranging the equation, we have:
p = h / λ
Substituting the given wavelength (λ = 5.37 x 10^-7 m) and Planck's constant (h), you can calculate the momentum (p) of the electron. Since the momentum equals the product of mass and velocity, you can rearrange this equation to solve for velocity:
p = m * v
Rearranging again to solve for v:
v = p / m
Note that the mass of an electron is approximately 9.109 x 10^-31 kg.
(b) To find the wavelength given the speed of the electron, you can utilize the de Broglie equation. Rearranging it, we get:
λ = h / p
Again, using Planck's constant (h) and substituting the given velocity (v = 3.80 x 10^6 m/s), we can calculate the momentum (p) of the electron. Then, substitute the momentum value into the de Broglie equation to determine the wavelength (λ) of the electron.
In both cases, the de Broglie equation is the key equation to use.