Problems

Potassium chloride (KCl) is a molecule formed by an ionic bond. At equilibrium separation the atoms are $r_0=0.279\text{nm}$ apart. Determine the electrostatic potential energy of the atoms.

The measured energy dissociated energy of KCl is 4.43 eV. Use the results of the preceding problem to determine the energy of repulsion of the ions due to the exclusion principle.

For the preceding problem, find the equilibrium separation of the H and Cl atoms. Compare this with the actual value.

The characteristic energy of the ${\text{N}}_2$ molecule is $2.48\times {10}^{\mathrm{-4}}\text{eV}$. Determine the separation distance between the nitrogen atoms

A diatomic ${\text{F}}_2$ molecule is in the $l=1$ state. (a) What is the energy of the molecule? (b) How much energy is radiated in a transition from a $l=2$ to a $l=1$ state?

The CsI crystal structure is BCC. The equilibrium spacing is approximately $r_0=0.46\text{nm}$. If ${\text{Cs}}^{+}$ ion occupies a cubic volume of $r_0^3$, what is the distance of this ion to its “nearest neighbor” ${\text{I}}^{+}$ ion?

The measured density of a NaF crystal is $2.558{\text{g/cm}}^3$. What is the equilibrium separate distance of ${\text{Na}}^{+}$ and ${\text{Fl}}^{\text{−}}$ ions?

Determine the dissociation energy of 12 moles of sodium chloride (NaCl). (Hint: the repulsion constant n is approximately 8.)

What value of the repulsion constant, n, gives the measured dissociation energy of 171 kcal/mol for KCl?

What is the difference in energy between the $n_x=n_y=n_z=4$ state and the state with the next higher energy? What is the percentage change in the energy between the $n_x=n_y=n_z=4$ state and the state with the next higher energy? (b) Compare these with the difference in energy and the percentage change in the energy between the $n_x=n_y=n_z=400$ state and the state with the next higher energy.

What value of energy corresponds to a density of states of $1.10\times {10}^{24}{\text{eV}}^{\mathrm{-1}}$ ?

Consider a cube of copper with edges 1.50 mm long. Estimate the number of electron quantum states in this cube whose energies are in the range 3.75 to 3.77 eV.

Determine the Fermi energy and temperature for copper at $T=0\text{K}$.

What is the main difference between an insulator and a semiconductor?

A valence electron in a crystal absorbs a photon of wavelength, $\lambda =0.300\text{nm}$. This is just enough energy to allow the electron to jump from the valence band to the conduction band. What is the size of the energy gap?

Suppose that the cross-sectional area of the strip (the area of the face perpendicular to the electric current) presented to the in the preceding problem is $1{\text{mm}}^2$ and the current is independently measured to be 2 mA. What is the number density of the charge carriers?

The Hall effect is demonstrated in the laboratory. A thin rectangular strip of semiconductor with width 5 cm and cross-sectional area $2{\text{mm}}^2$ is attached to a battery and immersed in a field perpendicular to its surface. The Hall voltage reads 12.5 V and the measured drift velocity is 50 m/s. What is the magnetic field?

A p-n diode has a reverse saturation current $1.44\times {10}^{\mathrm{-8}}\text{A}$. It is forward biased so that it has a current of $6.78\times {10}^{\mathrm{-1}}\text{A}$ moving through it. What bias voltage is being applied if the temperature is 300 K?

Applying the positive end of a battery to the p-side and the negative end to the n-side of a p-n junction, the measured current is $8.76\times {10}^{\mathrm{-1}}\text{A}$. Reversing this polarity give a reverse saturation current of $4.41\times {10}^{\mathrm{-8}}\text{A}$. What is the temperature if the bias voltage is 1.2 V?

At what temperature, in terms of $T_C$, is the critical field of a superconductor one-half its value at $T=0\text{K}$ ?

A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a $50\text{-}\text{Ω}$ resistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?