Examstyle Questions: Wave Particle Duality and Electron Energy Levels

The diagram show part of the energy level diagram for an atom.
There are four energy levels, labelled A, B, C and D. The atom is initially in energy level D. An electron of energy 3.0 eV collides with the atom. This causes the atin to change energy.
a) i) If the collision raises the atom to energy level B, how much energy is the colliding electron left with?
energy = ......................... eV
(1 Mark)
ii) Which energy level ( A, B or C ) will the atom definitely not be in after the collision?
energy level = ..........................
(1 Mark)
((Marks available: 2)

The kinetic eneryg of the electron in a ground state hydrogen atom is +2.2 x 10^{18} J.
a) Show that this suggests an electron momentum of 2.0 x 10^{24} kg m s^{1}.
me = 9.1 x 10^{31} kg
(3 Marks)
b) Show that the de Broglie wavelength for an electron with this momentum is about 3 x 10^{10} m.
h = 6.6 x 10^{34} J s.
(2 Marks)
((Marks available: 5)

In 1924, Prince Louis de Broglie suggested that all moving particles demonstrate wavelike behaviour.
a) State the de Broglie equation and define all the symbols.
(2 Marks)
b) Neutrons may be used to study the atomic structure of matter. Diffraction effects are noticeable when the de Broglie wavelength of the neutrons is comparable to the spacing between the atoms. This spacing is typically 2.6 x 10^{10} m.
i) Suggest why using neutrons may be preferable to using electrons when investigating matter.
(1 Mark)
ii) Calculate the speed v of a neutron having a de Broglie wavelength of 2.6 x 10^{10} m. The mass of a neutron is 1.7 x 10^{27} kg.
v = ............................. m s^{1}
(3 Marks)
(Marks available: 6)
Answer outline and marking scheme for question:

a) 3.0  2.5 = 0.5 eV
(1 Mark)
b) A
(1 Mark)
(Marks available: 2)

a) p = mv
v = 2.0 x 10^{24} / 9.1 x 10^{31} = 2.2 x 10^{6} m s^{1}
Ek = 0.5mv^{2} = 0.5 x 9.1 x 10^{31} x (2.2 x 10^{6})^{2}
(= 2.2 x 10^{18} J)
(3 Marks)
b) λ = h/p
λ = 6.6 x 10^{34} / 2.0 x 10^{24} = 3.3 x 10^{10} m
(2 Marks)
(Marks available: 5)

a)
λ = h / λ = h mv p λ = wavelength, h = Planck constant,
m = mass (of particle) and v = speed / velocity OR p = momentum
(2 Marks)
b) i) Neutrons have no charge / Neutrons experiences no electrical forces (ora)
(1 Mark)
ii) 2.6 x 10^{10} = 6.63 x 10^{34} / mv / mv = 2.55 x 10^{24} (kgms^{1})
v = 6.63 x 10^{34} / (2.6 x 10^{10} x 1.7 x 10^{27}) / v = 2.55 x 10^{24} / 1.7 x 10^{27}
v = 1.5 x 10^{3} (ms^{1}) (Allow uae of m_{n} = 1.67 x 10^{27} kg)
(3 Marks)
(Marks available: 6)