Consider 1.50 mols of a substance in thermal equilibrium at a temperature of 87.0 °C whose atoms can occupy only two energy levels separated by 5.00x10² eV, where 1 eV (electron volt) is an energy unit equal to 1.60x1019 J. ks = 1.38x1023 J/K , Na = 6.02x10²³ mol1 Eg a) Find the probability of occupation of the ground state with energy E1 and the 1st excited state with energy E2? b) How many atoms in the substance (on average) are in 5.00x10? ev the ground state and in the 1st excited state? E1

The characteristic vibrational temperature for chlorine (Cl₂) gas is 805 K. Calculate the fraction of chlorine molecules in the first excited vibrational state (v-1) when the temperature is 1610 K.

Question 9. While most transition metals have work functions corresponding to photon frequencies that are larger (higher) than visible light, alkali and alkaline earth metals have low-energy work functions. For example, calcium has a work function of o = 4.3419×10-19 J. (a) What is the initial state n, for the hydrogen emission lines at visible wavelengths (i.e., those with n = 2) for the lowest-energy photon that would eject an electron from calcium? %3! (b) If the colors of the visible hydrogen emission lines (n; = 3 to n = 6) are red, green, blue and %3D violet, which colors are capable of ejecting the electrons from calcium? (c) The energy of the emitted photon you identified in part (a), is not identical to the workfunction of calcium. Therefore, the electron is ejected from the metal surface with some kinetic energy (i.e., energy is conserved in the photoelectric effect process). What would the velocity of the electron ejected from calcium (in meters per second)?

Suppose that you have a solution containing a substance whose molecule has two quantum states corresponding to different orientations of a certain subgroup of atoms. The energy difference between these two molecular states is ΔE = 0.10 eV. You are running an experiment where no more than 5% percent of the molecules can be in the higher-energy state, or it will cause unacceptable noise. Can you run the experiment at room temperature, or do you need to cool your solution?