Problem 1
If the energy of the \(H_{2}\) covalent bond is -4.48 eV, what wavelength of light is needed to break that molecule apart? In what part of the electromagnetic spectrum does this light lie?
Problem 2
An Ionic Bond. (a) Calculate the electric potential energy for a K\(^+\) ion and a Br\(^-\) ion separated by a distance of 0.29 nm, the equilibrium separation in the KBr molecule. Treat the ions as point charges. (b) The ionization energy of the potassium atom is 4.3 eV. Atomic bromine has an electron affinity of 3.5 eV. Use these data and the results of part (a) to estimate the binding energy of the KBr molecule. Do you expect the actual binding energy to be higher or lower than your estimate? Explain your reasoning.
Problem 5
A hypothetical NH molecule makes a rotational-level transition from \(l\) = 3 to \(l\) = 1 and gives off a photon of wavelength 1.780 nm in doing so. What is the separation between the two atoms in this molecule if we model them as point masses? The mass of hydrogen is 1.67 \(\times\) 10\(^-$$^2$$^7\) kg, and the mass of nitrogen is 2.33 \(\times\) 10\(^-$$^2$$^6\) kg.
Problem 7
The water molecule has an \(l\) = 1 rotational level 1.01 \(\times\) 10\(^-$$^5\) eV above the \(l\) = 0 ground level. Calculate the wavelength and frequency of the photon absorbed by water when it undergoes a rotational-level transition from \(l\) = 0 to \(l\) = 1. The magnetron oscillator in a microwave oven generates microwaves with a frequency of 2450 MHz. Does this make sense, in view of the frequency you calculated in this problem? Explain.
Problem 8
Two atoms of cesium (Cs) can form a Cs \(_{2}\) molecule. The equilibrium distance between the nuclei in a \(\mathrm{Cs}_{2}\) molecule is \(0.447 \mathrm{nm} .\) Calculate the moment of inertia about an axis through the center of mass of the two nuclei and perpendicular to the line joining them. The mass of a cesium atom is \(2.21 \times 10^{-25} \mathrm{~kg}\).
Problem 13
When a hypothetical diatomic molecule having atoms 0.8860 nm apart undergoes a rotational transition from the \(l\) = 2 state to the next lower state, it gives up a photon having energy 8.841 \(\times\) 10\(^-$$^4\) eV. When the molecule undergoes a vibrational transition from one energy state to the next lower energy state, it gives up 0.2560 eV. Find the force constant of this molecule.
Problem 17
The maximum wavelength of light that a certain silicon photocell can detect is 1.11 \(\mu\)m. (a) What is the energy gap (in electron volts) between the valence and conduction bands for this photocell? (b) Explain why pure silicon is opaque.
Problem 18
The gap between valence and conduction bands in diamond is 5.47 eV. (a) What is the maximum wavelength of a photon that can excite an electron from the top of the valence band into the conduction band? In what region of the electromagnetic spectrum does this photon lie? (b) Explain why pure diamond is transparent and colorless. (c) Most gem diamonds have a yellow color. Explain how impurities in the diamond can cause this color.
Problem 19
The gap between valence and conduction bands in silicon is 1.12 eV. A nickel nucleus in an excited state emits a gammaray photon with wavelength 9.31 \(\times\) 10\(^-$$^4\) nm. How many electrons can be excited from the top of the valence band to the bottom of the conduction band by the absorption of this gamma ray?
Problem 25
For a solid metal having a Fermi energy of 8.500 eV, what is the probability, at room temperature, that a state having an energy of 8.520 eV is occupied by an electron?
