Suppose do an experiment where a beam of electrons is direct

Suppose do an experiment where a beam of electrons is directed of a crystal lattice. A screen placed above the crystal records the positions of the directed electrons. From your measurements of where electrons land, you you determine that the average wavelength of the electrons is 1.67 A. What must be the average momentum of the electrons? On average, hoe fast must the electrons be moving? (The mass of an electron is 9:11 times a0^-31 kg.) Suppose your experimental uncertainity in the momentum was about 10%. According to the uncertainity Principle, hoe precisely could you locate the electrons?

Solution

28.

a) wavelength, lambda = 1.67 A = 1.67 x 10^-10 m

lambda = h / p

p = h / lambda = (6.626 x 10^-34 ) / (1.67 x 10^-10)

p = 3.968 x 10^-24 kg m/s

b) p = m v

3.968 x 10^-24 = 9.109 x 10^-31 x v

v = 4356131.3 m/s

c) deltap deltax = h / 2 pi

(10 x 3.968 x 10^-24 / 100) ( deltax) = (6.626 x 10^-34 / 2 pi)

deltax = 2.658 x 10^-10 m