Concept explainers
The number of electrons can be placed in the
Answer to Problem 1OQ
The number of electrons can be placed in the
Explanation of Solution
In this case, the principal quantum number,
Write the expression for the orbital quantum number,
Here,
Write the expression for the orbital magnetic quantum number,
Here,
In this case, there are
Here,
Write the expression for the total possible values for each value of the orbital quantum number,
Here,
Write the expression for the grand total of
Conclusion:
Substitute
So, the possible values of orbital magnetic quantum number,
Substitute
Substitute
Substitute
Substitute
Thus, the number of states are
Therefore, the number of electrons can be placed in the
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Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
- A hypothetical atom has only two atomic energy levels, separated by 3.2 eV. Suppose that at a certain altitude in the atmosphere of a star there are 6.1 * 1013/cm3 of these atoms in the higher-energy state and 2.5 * 1015/cm3 in the lower-energy state. What is the temperature of the star’s atmosphere at that altitude?arrow_forwardYou are working on determining the angle that separates two hybridized orbitals. In the process of determining the coefficients in front of the various atomic orbitals, you align the first one along the z-axis and the second in the x/z-plane (so o = 0). The second hybridized orbital was determined to be: W2 = R1s + R2p, sin 0 + R2p, cos 0 Determine the angle, 0, in degrees to one decimal place (XX.X) that separates these two orbitals. Assume that the angle will be between 0 and 90 degrees.arrow_forward2. a) Problem 8.3 of Textbook: Calculate the frequency of the hydrogen transition n = 101 → n = 100. b) A light photon emitted from a higher energy level ofn = 3 to a lower energy level of n = 2 in hydrogen has a wavelength of 1 = 656.3 nm. Compute the atom distribution ratio N3/N2 at the equilibrium when temperatures are T = 102K.arrow_forward
- An electron is in the hydrogen atom with n = 5. (a) Find the possible values of L and Lz for this electron, in units of h. (b) For each value of L, find all the possible angles between L → and the z-axis. (c) What are the maximum and minimum values of the magnitude of the angle between L →and the z-axis?arrow_forward3. Consider a monatomic linear with equilibrium separation a. Suppose the outer electrons (of mass m) in a given atom move with a displacement different from that of the corresponding ion core (of mass M). Let the displacement of the ion core s be: Us = uei(Ksa-wt) and the displacement of the center of mass of the outer electrons associated with ion s be: V = vei(Ksa-wt) Each ion core is assumed to interact only with its own outer electrons with a force proportional to the displacement of the electron distribution from the nucleus, and the force constant is C₂. However, neighboring electron distributions interact with a force constant C₁. a) Show that -w² Mus = C₂ (vs - Us) -w²mvs = C₂ (us - Vs) + C₁ (Vs+1 + Vs-1-2vs) b) Substitute for the displacements, and solve the resulting simultaneous equations. Find an expression for w². c) Take the limit as m → 0 (the mass of electrons is much smaller than that of the ion core), and show that the dispersion relation for the acoustic mode is…arrow_forwardIf the orbital angular momentum of an atom is 2 and the perpendicular momentum is 5/2, then the number of possible values of the total angular momentum are 10:35 صarrow_forward
- Angular 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_forwardThe electron in a hydrogen atom occupies the orbital state |2, -1> and the spin state |1/2, -1/2>. what are the possible states? a. None O b. [5/2,-1/2> and 13/2,-3/2> O c. [5/2,-1/2> and |3/2,-1/2> O d. [5/2,-3/2> and |3/2,-1/2> e. [5/2,-3/2> and |3/2,-3/2>arrow_forwardFor an electron in a hydrogen atom in the n=2 state, compute: (a) the angular momentum; (b) the kinetic energy; (c) the potential energy; and (d) the total energy.arrow_forward
- Form factor of atomic hydrogen. For the hydrogen atom in its ground state, the number density is n(r) = (ra)¯ exp(-2r/a), where a, is the Bohr radius. Show that the form factor is fc = 16/(4 + G*a)*. %3Darrow_forward9. An atom in a solid has two energy levels: a ground state of degeneracy gi and an excited state of degeneracy g2 with an energy A above the ground state. (a) Show that the partition function for the atom, Zatom; is Zatom = 91 + »e¬ßA (b) Show that the heat capacity of the atom is given by 9192A²e¬BA kgT² (g1 + g2e-BA)² (c) Show that a monatomic gas of these atoms has a partition function of Z = ZatomZN Where only translational motion of the gaseous atoms is considered so that N V ZN =arrow_forward(a) The doubly charged ion N2+ is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the N2+ ion? (b) Estimate the energy of the least strongly bound level in the L shell of N2+. (c) The doubly charged ion P2+ is formed by removing two electrons from a phosphorus atom. What is the ground-state electron configuration for the P2+ ion? (d) Estimate the energy of the least strongly bound level in the M shell of P2+arrow_forward
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