Discuss the differences between the rotational and vibrational energy levels of the deuterium (“heavy hydrogen”) molecule D2 and those of the ordinary hydrogen molecule H2. A deuterium atom has twice the mass of an ordinary hydrogen atom.

The mass of the most common silicon atom is 4.646 * 10-26 kg, and the mass of the most common oxygen atom is 2.656 * 10-26 kg. When a molecule of silicon monoxide (SiO) makes a transition between the l = 1 and l = 0 rotational levels, it emits a photon of wavelength 6.882 mm. Find the distance between the Si and O nuclei.

An  atom has a mass of 1.17 × 10-26 kg.  If we consider this atom vibrating with simple harmonic motion with a force constant of  k =49.8 N/m (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, ħ = 1.055 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) Determine the  ground state energy of this system, in hundredths of electron Volts. (answer x 10-2 eV).  Please give your answer with two decimal places.

There exists in nature a particle known as the muon. It is just a heavy electron with a mass mµ = 207me. It decaysin 10−6seconds. Suppose there exists a molecule analogous to H+2(two protons + 1 electron), but with the electronreplaced by a muon:(a) Find the equilibrium separation of the nuclei (R0) in such a molecule.(b) If a rotational state is excited, estimate the wavelength of the emitted radiation in the transition to the groundstate

Estimate kBT at room temperature, and convert this energy into electronvolts (eV). Using this result, answer the following: (a) Would you expect hydrogen atoms to be ionized at room temperature? (The binding energy of an electron in a hydrogen atom is 13.6 eV.) (b) Would you expect the rotational energy levels of diatomic molecules to be excited at room tem￾perature? (It costs about 10−4 eV to promote such a system to an excited rotational energy level.)