Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 44, Problem 14SP
To determine
The number of electrons in an aluminum atom, the atomic number, and number of electrons for principle quantum number
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How many electrons can occupy the system with l=0, l=2 and l=4. What is number of possible orientations of the orbital angular momentum with l=4? What is the smallest z-component of the orbital angular momentum?
A hydrogen atom has energy -1.36 × 10-19 J, and the electron can be in any one of ten different quantum states. Find the spectroscopic notation for this atom.what is the principal quantum number? What is total orbital angular momentum? What is maximum z. Direction total angular momentum? What is degeneracy ?
1.
a. What is the total number of orbitals associated with the principal quantum number n=1?
b. What is the total number of orbitals associated with the principal quantum number n=2?
c. What is the total number of orbitals associated with the principal quantum number n=3?|
d. What conclusion can be drawn from total number of orbitals associated with a given principal
quantum number?
2. List the values of n, {, m, for an orbital in the 4d subshell.
Chapter 44 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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- (a) What is the minimum value of l for a subshell that contains 11 electrons? (b) If this subshell is in the n = 5 shell, what is the spectroscopic notation for this atom?arrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², 1 = 0,1,2,..., n-1 Lz = m₂ħ, m₁ = 0, ±1, ±2,..., ±l 3 S² = s(s+1)h² = h², 4 Consider an excited electron (n > 1) on an H-atom. Sz = msh 1 =+=ħ Show that the minimum angle that the I can have with the z-axis is given by n-1 n L.min = cos Clue: the angle a vector with magnitude V from the z-axis can be computed from cos 0 = V²/Varrow_forwardAngular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.arrow_forward
- a. Is a 4p → 4s transition allowed in sodium? If so, what is its wavelength? If not, why not?b. Is a 3d → 4s transition allowed in sodium? If so, what is its wavelength? If not, why not?arrow_forwardA doubly ionized lithium atom (Li++) is one that has had two of its three electrons removed. The energy levels of the remaining single-electron ion are closely related to those of the hydrogen atom. The nuclear charge for lithium is +3e instead of just +e. How are the energy levels related to those of hydrogen? How is the radius of the ion in the ground level related to that of the hydrogen atom? Explain.arrow_forwardConsider the radial wave function for a hydrogenic system: n = 7 50 100 150 200 r a. What is the angular momentum letter of the orbital? b. What is the numerical value of the magnitude of the orbital angular momentum? For h use the value 1.0545718 × 10-34 Js. Js c. What are the possible values of the quantum number for the z-component of the orbital angular momentum? Enter as a comma separated list from least to greatest (e.g. ...,-1,0,1,2,... ): d. Is there a difference in the electron's energy if it were in an 4p orbital instead of the orbital it is actually in as indicated by the above wave function? yes no N psi(x) -0.1 0.1 0.2 0.3arrow_forward
- An electron in hydrogen is in the 5ff state. A) Find the largest possible value of the z component of its angular momentum. Express your answer in terms of ℏℏ. B) For the electron in part A, find the value of the expression L2x+L2y−−−−−−−√Lx2+Ly2. Express your answer in terms of ℏℏhbar.arrow_forwardWhat is the energy of the photon that, when absorbed by a hydrogen atom, could cause an electronic transition from the n = 2 state to the n = 5 state? Answer in units of eV. What energy could cause an electronic transition from the n = 5 state to the n = 8 state? Answer in units of eV.arrow_forwardWe want to look at the angular momentum structure of one electronic level of an atom. a. The atom has orbital angular momentum L, electron spin angular momentum S and nuclear angular momentum I. For very large magnetic fields B, what are the quantum numbers and energies? b. In addition to the static B field along the z axis, we add a transverse oscillating magnetic field. Which states are now coupled by the oscillating field, i.e. between which states are transitions induced?arrow_forward
- Consider only the transitions involving the first four energy levels for a hydrogen atom:a. How many emissions are possible for an electron in the n = 4 level as it goes tothe ground state?b. Which electronic transition is the lowest energy?c. Which electronic transition corresponds to the shortest wavelength emissionarrow_forward2. Question 2: a. In your schematic of the hydrogen atom, draw the transition of the electron from the n=1 level to the n=2 level. Label whether the electron gains or loses energy in this transition? 1 b. Find the energy difference between the n=1 level and the n=2 level. Relate this value back to Q1 to make sense of whether the n=1 level or the n=2 level is the lowest energy state. 1/3arrow_forwarda. What is the length of a p electron's angular momentum vector? b. List the possible z components. c. What are the values of the angle that the angular momentum vector makes with the z axis? d. Draw a picture showing all possible orientations of the angular momentum for p electron. 3.arrow_forward
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