An electron has the same de Broglie wavelength as a 1.8 eV photon.The speed of the electron is closest to:
A)1100 m/s
B)980 m/s
C)910 m/s
D)840 m/s
E)770 m/s

Question

Quizplus · Accepted Answer

The de Broglie wavelength of a particle is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. The momentum of a photon is given by p = h/λ, where λ is the wavelength of the photon. The kinetic energy of an electron is given by KE = 1/2 mv^2, where m is the mass of the electron and v is its speed. We can use these equations to find the speed of the electron.λ_electron = λ_photon = h/pp_electron = h/λ_electron = h/(h/p_photon) = p_photonKE_electron = 1/2 mv^2 = p^2/2m = (p_photon)^2/2mv = sqrt(2KE_electron/m) = sqrt(2(1.8 eV)(1.602 x 10^-19 J/eV)/(9.109 x 10^-31 kg)) = 1100 m/s

An Electron Has the Same De Broglie Wavelength as a 1.8