Question

1. If electrons are quantized particles that behave like waves then based on the deBroglie hypothesis their kinetic energy is well defined. (a) Determine the energy and wavelength of free electrons (electrons in vacuum or those not confined in an atom) accelerated by a potential difference of 100 kV b) Do the same calculation for electrons with a potential energy of 1 eV (c) On the the other hand electrons trapped in a typical solid, such as a conducting metal, have negative energies with respect to free electrons in space. If the ionization energy of the valence electrons in a carbon atom is about 10 eV, use the hydrogen model of an atom to estimate the diameter of a carbon atom.

Answer 1

Energy=charge*potential difference

1.6*10^-19*100000=1.6*10^-14J=100keV

E=hc/lambda

lambda=1242/100000

=.012nm

b)When energy is 1eV

lambda=1242/1=1242nm