Question

Useful information: The resolving power of a microscope is directly proportional to the wavelength. For relativistic conditions Epem K E-me, where m is the rest mass. For the electron m 0.511 MeV. Starting at rest find over what potential do you need to accelerate the electrons 4) Use the Heisenberg uncertainty principle to estimate the minimum velocity of a proton or neutron in a Lead-208 nucleus, which has a diameter of about 13 fm (1 fm- 10-15 m). Assume that the speed is non-relativistic, and then check at the end whether this assumption was appropriate. 5) The kinetic energy of an electron in an orbit of the hydrogen Bohr atom is 1.35x10" J. Assume non-relativistic speeds. a) What orbit does the electron occupy?

quantum mechanics number 4 only.

Answer 1

Using certainty principle we get delta x middot delta px greaterthanorequalto hstrok/2 delta px = m delta v_x therefore delta x = 13fm mass of pb(lead) = 208 delta v_x = hstrok/2m delta x Vertical-bar max for minimum velocity delta r should be maximum hstrok plusminus h/2v + 6.67 times 10^-34 /2r (plank's constant) so delta V_x Vertical-bar min = 6.67 times 10^-34 /2 times 208 times 2 times 3.14 times 13 times 10^-15 delta v_x = 6.67 times 10^-19 /52 times 208 times 3.14 d4elta v_x = 1.963 times 10^-4 times 10^-19 delta V_x = 1.96 times 10^-23 m/sec so minimum velocity is that V = 1.963 times 10^-23 m/sec (should be small)