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Calculate the de Broglie wavelength of a typical nitrogen molecule in the atmosphere on a hot summer day (37°C). Compare this with the diameter (less than 1 nm) of the molecule.

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Calculate the velocities of electrons with de Broglie wavelengths of 1.7×103 nm and 5.0 nm, respectively.
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)?
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A single electron ion MZ-1)+ with atomic number Z<84 emits a photon during an unknown electronic transition from some initial state n; to some final state nf. The photon then strikes an osmium surface, which has a work function O = 5.93 eV and causes an electron to be emitted. Many such photons create a beam of electrons (all with the same kinetic energy) that is directed at a single crystal nickel sample at normal incidence. The electrons are scattered from the crystal and it is observed that they do so with only two (2) non-zero diffraction angles (i.e., 2 different values of 0). From the DeBroglie-Bragg relation it is determined that the diffraction corresponds to a lattice spacing of a = 352.4 pm.
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