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Chapter 10: Q25E (page 467)
Formulate an argument explaining why the even wave functions in Fig 10.1 should be lower in energy than their odd partners.
The wave function that has more anti-nodes is at a higher energy.
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Question: The diagram shows the energy bands of a tunnel diode as the potential difference is increased. In this device high impurity atom density causes the occupied donor and unoccupied acceptor levels to spread into impurity bands which overlap respectively the n-type conduction- and the p-type valence bands. In all unbiased diodes, the depletion zone between the n-type and p-type bands constitutes a potential barrier (see Section 6.2) but in the tunnel diode it is so thin that significant tunnelling occurs. The current versus voltage plot shows that unlike a normal diode significant current begins to flow as soon as there is an applied voltage—before the bias voltage is Egap /e. It then decreases (so called negative resistance) before again increasing in the normal way. Explain this behavior.
Sketch an energy-versus-position diagram. Complementary to Figure 10.4, showing valence hole motion a conduction electron participation in an operating pnp transistor.
Electron affinity is a property specifying the "appetite" of an element for gaining electrons. Elements, such as fluorine and oxygen that lack only one or two electrons to complete shells can achieve a lower energy state by absorbing an external electron. For instance, in uniting an electron with a neutral chlorine atom, completing its n = 3 shell and forming a CI ion, 3.61 eV of energy is liberated. Suppose an electron is detached from a sodium atom, whose ionization energy is 5.14 eV.Then transferred to a (faraway) chlorine atom.
(a) Must energy on balance be put in by an external agent, or is some energy actually liberated? If so How much?
(b) The transfer leaves the sodium with a positive charge and the chlorine with a negative. Energy can now be extracted by allowing these ions to draw close forming a molecule. How close must they approach to recover the energy expended in part (a)?
(c)The actual separation of the atoms in a NaCl molecule is 0.24 nm. How much lower in energy is the molecule than the separated neutral atoms?
The bond length of the molecule is , and its effective spring constant is at room temperature.
(a) What would be the ratio of molecules with rotational quantum number to those with (at the same vibrational level), and
(b) What would be the ratio of molecules with vibrational quantum number to those with (with the same rotational energy)?
By expanding an arbitrary in a power series about a local minimum assumed to be at , prove that the effective spring constant is given by equation .
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