Concept explainers
The Stark effect is the change in energy of a system due to the presence of an electric field (discovered by German physicist Johannes Stark in 1913). Consider the hydrogen atom. Its normally spherical
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Physical Chemistry
- What are the degeneracies of the H atom wavefunctions when spin is accounted for? Give a general formula.arrow_forwardAre mathematical expressions for the following potential energies positive or negative? Explain why in each case. a The attraction between an electron and a helium nucleus b The repulsion between two protons in a nucleus c The attraction between a north and a south magnetic pole d The force of gravity between the Sun and Earth e A rock perched on the edge of a cliff with respect to the base of the cliffarrow_forwardWhat experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?arrow_forward
- Consider an electron in the N shell. Express your answers in terms of h and in SI units. (a) What is the smallest orbital angular momentum it could have? (b) What is the largest orbital angular momentum it could have? (c) What is the largest orbital angular momentum this electron could have in any chosen direction? (d) What is the largest spin angular momentum this election could have in any chosen direction?arrow_forwardNow consider an excited state of He atom with electron configuration 1s' 2s'. In general, the wavefunction is a state: V (r, 0, 6, 02) = V(r, 0, ø)Vo. where V(r, 0, ø) and V, represent the spatial and the spin part. The spatial part is constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, 6) and ø (r, 0, 6), where subscript k denotes which electron it belongs to (i.e., k is either 1 or 2 since we have two electrons). • The spatial part of the wavefunction can be written 1*(r, 0, 4)o3* (r, 0, 4) + o(r, 0, ¢)o²*(r, 0, 4) V2 F (r, 0, 4)«3"(r, 0, ø) – 05" (r, 0, 4)o²°(r, 0, ø) V2 V2(r, 0, 6) = Vī2(r, 0, 6) = Explain (and demonstrate) which spatial wavefunction (V2(r, 0, 0) or V2(r, 0, 0)) is symmetric with respect to exchange of two electrons? Which one corresponds to the singlet and triplet state (defined by the spin multiplicity)? • Based on you response to the previous question, write down the wavefunction for the (i) ground state of He and the (ii) singlet…arrow_forwardVanadium tetrachloride (VCl4 ) is a bright red colored liquid with a vapor pressure of 5x10-2 torr at 298K. State the Jahn Teller Theorem and briefly discuss whether or not VCl4(g) is expected to manifest a Jahn Teller effect . What is the expected orbital angular momentum in the ground state of VCl4(g) ?arrow_forward
- The 4fz(x2-y2) orbital has the angular function Y = (constant)z(x^2-y^2)/r^3a. How many radial nodes does this orbital have?b. How many angular nodes does it have?c. Write equations to define the angular nodal surfaces. What shapes are these surfaces?arrow_forwardIf an orbital has an orbital angular momentum (Azimuthal) quantum number of four (4), what are the possible values of the magnetic quantum number?arrow_forward2.) Neglecting electron-electron repulsion, write down the singlet and triplet excited states of with the electron configuration, 1s^ 1 2s^ 1 . Make sure the wave function including spin and space parts) is antisymmetric under the interchange of the two electrons. What are the energies of the singlet and triplet states? What are the term symbols for the singlet and triplet states?arrow_forward
- 3. In which case the superposition principle holds for the energy of the electric field?arrow_forwardV7.arrow_forwardThe nucleus of a boron-11 atom has a spin (s) quantum number of 3/2. Calculate the magnitude of the spin vector as well as the possible values it can take for the z-component of the spin vector? Is boron-11 a boson or fermion?arrow_forward
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