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
- 1. The angular portions of the wave functions for the px and dxz orbitals of the hydrogen atom are linear combinations of the spherical harmonics and are given by the expressions below. 3 YP. = √(x²+x¹) = -sin coso 4T Wd₂ = 1/2 (Y/² + X/₂ ¹) = eigenfunctions of 15 4π These combinations are chosen to yield real functions. Are these functions a Ĺ sincoscoso -iħ. do ?arrow_forwardConsider 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_forwardExplain the origin of the spin–orbit coupling in atoms and discuss how it gives rise to different angular momentum coupling schemes.arrow_forward
- Consider the ground-state electron configurations of the atoms with the following atomic numbers: 7, 20, 26, 32, 37, 41, 85, 96. Calculate the total spin quantum number S for each, as well as its magnetic moment in Bohr magnetons.arrow_forwardWrite down the normalized determinantal wave function (slater determinant) of a He atom at its ground energy state. He atom has an electron configuration of 1s^2. Using the Slater determinant you ovtained above, prove that the He wave function is anti-symmetricarrow_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_forward
- Consider the atom having the electron configuration 1s 2s 2p 3s2 3p. Assume that the z components of both the orbital and spin angular momenta of the electron in the 3p subshell are positive. What are the quantum numbers that describe the state of this electron? a) O n = 3,1 = 2, m = 1, s = 1/2 b) On = 3,1 = 1, m = 1, s = 1/2 c) On = 3,1 = 1, m = –1, s = 1/2 d) O n = 3,1 = 2, m = 2, s = -1/2 n = 3,1 = 1, m = 2, s = 1/2 %3D e)arrow_forward(i) What do you understand by the dual nature of light? Explain clearly in few sentences. (ii)What is the difference between an emission and an absorption spectra? (iii) What is meant by Heisenberg uncertainty principle? Explain clearly in as simple a language as possible. (iv)What are the quantum numbers? How many are there ? What are their symbols and what do they signify? (v)What do you mean by periodic properties? What are the different trends seen in a periodic table and how can you explain them in at least two to three simple sentences for each of them?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
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