1.) In a Rutherford scattering experiment, an α-particle (charge = +2e) heads directly toward a gold nucleus (charge = +79 e). The -particle had a kinetic energy of 4.9 MeV when very far (r -> ∞ ) from the nucleus. Assuming the gold nucleus to be fixed in space, determine the distance of closest approach. (Hint: Use conservation of energy with PE = keq1q2/r.)
2.) What is the energy of the photon that, when absorbed by a hydrogen atom, could cause the following?
(a) an electronic transition from the n = 2 state to the n = 4 state
(b) an electronic transition from the n = 4 state to the n = 7 state
3.) Two hydrogen atoms collide head-on and end up with zero kinetic energy. Each then emits a 121.6 nm photon (n = 2 to n = 1 transition). At what speed were the atoms moving before the collision?
(a) Find the energy of the electron in the ground state of triply ionized beryllium, which has an atomic number Z = 4.
(b) Find the radius of its ground-state orbit.
5.) The K-shell ionization energy of copper is 8979 eV. The L-shell ionization energy is 951 eV. Determine the wavelength of the K_α emission line of copper. What must the minimum voltage be on an x-ray tube with a copper target in order to see the K_α line?
Five questions of modern physics regarding Scattering, Bohr's model, collision of atoms, energy of electron, and k-shell and L-shell ionization are solved with full explanations.