Question

10. Consider the wavefunction Be-ibx for a free electron, of mass 9.1 x 10-31 kg, whose de Broglie wavelength is 1 nm (where B and b are positive real constants). a) What is the momentum of the electron? b) What is the value of b? c) What is the value of (Kx)?

Answer 1

a) momentum and wavelength of any particle are related by de-brogile formula

$\lambda =h/p\\ \implies p=h/\lambda\\ \implies p=\frac{6.626\times 10^{-34}}{1\times 10^{-9}}=6.626\times 10^{-25}Kgm/s$.

b) b is the wave number of the electron

$b=p/\hbar =6.28\times 10^9 m^{-1}$

c) $K_x$ is the wave vector in x-direction, it is nothing but b.

$K_x=b=6.28\times 10^9m^{-1}$