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Calculate the torque (magnitude and direction) about point $O$ due to the force $F$ in each of the cases sketched in $\textbf{Fig. E10.1.}$ In each case, both the force $F$ and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude $F =$ 10.0 N.
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?
For the H$_2$ molecule the equilibrium spacing of the two protons is 0.074 nm. The mass of a hydrogen atom is 1.67 $\times$ 10$^-$$^2$$^7$ kg. Calculate the wavelength of the photon emitted in the rotational transition $l$ = 2 to $l$ = 1.
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.
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.
The rotational energy levels of CO are calculated in Example 42.2. If the energy of the rotating molecule is described by the classical expression $K$ = \(\frac{1}{2}\) $I$$\omega$$^2$, for the $l$ = 1 level what are (a) the angular speed of the rotating molecule; (b) the linear speed of each atom; (c) the rotational period (the time for one rotation)?