Physics 2: Physical Science & Technology (PHYC10004)
Week 11
Discussion questions
1
What non-classical basic assumptions are made in the Bohr model of the hydrogen atom?
2
What does Bohr's correspondence principle say about quantum mechanics versus classical mechanics?
3
It’s easy to understand how two electrons (one spin up, one spin down) fill the n = 1 or K shell of a helium atom. How is it possible that eight more electrons are allowed in the n = 2 shell, filling the K and L shells for a neon atom?
Problem-solving questions
4
According to the Bohr model of the atom, the energies of an electron in a ‘hydrogen-like’ atom are given by:
where n is the principal quantum number, and Zis the atomic number of the atom.
a) Calculate the value of in units of eV [Hint: simplify the powers first].
b) Calculate the longest wavelength of a photon of visible light emitted in the Balmer (n = 2) series of hydrogen.
c) An atom of helium has Z = 2. One of its electrons is removed. It is now He+. These ions can also be raised to excited states, and in de-exciting to lower states, also emit radiation. Its spectral series can be called by the same three names as for the H spectra.
Calculate the lowest energy of a photon emitted in the Balmer series ofa He+ ion? What part of the electromagnetic spectrum will this photon be located in (visible, UV, infrared, etc)?
5
A hydrogen-like atom with Z = 4 and one electron is observed in an n = 100 state. Use Bohr theory to predict the size of the atom & the atom’s energy (in eV).
6
Doubly ionized lithium (usually designated LiIII) has one electron in orbit around a nucleus of charge +3e. What is the radius of the smallest Bohr orbit in doubly ionized lithium? What is the energy of this orbit?
7
How much energy is required to cause an electron in hydrogen to move from the n=1 state to the n=2 state? Suppose the atom gains this energy through collisions with hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy be great enough to excite the electron? (KB is Boltzmann’s constant).
8
The quantity is sometimes described as the fine structure constant. Calculate its value in S.I units, and state its unit.
9
Assume three identical uncharged particles of mass m and spin ½ are contained in a one- dimensional box of length L. What is the ground state energy of this system?
Past examination questions
10
Consider a hydrogen atom initially in its ground state (E = —13.6 eV, N = 1), as shown in the figure to the right.
a) Copy the figure and label the energies of the four most tightly bound states.
A photon from an external source is absorbed and excites the atom to the 3rd excited state (N = 4).
b) Draw an arrow on the diagram that corresponds to this transition.
c) What is the energy of the photon in electron volts?
d) In which part of the electromagnetic spectrum (radio wave, microwave, infrared, ultra-violet, X-ray or gamma ray) was this photon?
From the N = 4 state, the atom decays by emitting a photon of wavelength 486nm.
e) Calculate the momentum of the emitted photon.
11
The figure to left shows the binding energy i.e. the energy required to remove the least strongly bound electron of the light elements up to F, (Fluorine, Z=9).
a) Briefly explain the general trends indicated by the straight lines on this graph Include in your answer
i. The reasons for the large difference in ionization energies of He and Li
ii. The reason that the ionization energies gradually increase from Li to F.
b) Estimate the ionization energy of the next element in the series Ne (Neon, Z =10).
c) Provide an approximate value for the ionization energy of Na (Sodium Z=11) and explain your reasoning. (You may wish to consider the quantum numbers n, l and ml)
12
a) In classical physics an atom would not be stable because it would emit electromagnetic waves of frequency f, because the electron’s orbit, when seen edge on, appears to be an electric dipole. At what electron radius, in nm, would the electron emit light with a wavelength of 600 nm?
b) An electron is confined between two impenetrable walls 0.2 nm apart. Determine the energy levels for the states n =1, 2 and 3.
13
Schrodinger’s theory treats electrons in atoms as waves, and can be used to calculate their energies. When combined with Pauli’s exclusion principle, the theory is able to predict the number of electrons in a given quantum level and to account for the observed structure in the periodic table.
a) Explain the significance of the Pauli exclusion principle in the context of the shell structure of atoms.