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Chapter 5: Q14P (page 218)

The ground state of dysprosium (element 66, in the 6th row of the Periodic Table)

is listed as Is5. What are the total spin, total orbital, and grand total angular

momentum quantum numbers? Suggest a likely electron configuration for

dysprosium.

Short Answer

Expert verified

The total spin, orbital spin and total angular momentum are:

S=2;L=6;J=8.

Electronic configuration:

(1s)2(2s)2(2p)6(3s)2(3p)6(3d)10(4s)2(4p)6⏟definite(36electrons)(4d)10(5s)2(5p)6(4f)10(6s)2⏟likely(30electrons)

Step by step solution

01

Definition of total spin, total orbital and total angular momentum quantum number

Spin quantum number, the fourth quantum number introduced to explain the rotation and direction of the electron spin in space. By combining a particle's orbital and intrinsic angular momentum, the total angular momentum quantum number in quantum mechanics parameterizes the total angular momentum of a particular particle.

02

Determining the total spin, total orbital and grand total angular momentum quantum numbers

Ground state of dysprosium is 5l8. That means 2s + 1 = 5 and J = 8. So total spin , orbital spin and total angular momentum are:

S = 2, L = 6, J = 8.

Electronic configuration :

(1s)2(2s)2(2p)6(3s)2(3p)6(3d)10(4s)2(4p)6⏟definite (36 electrons)(4d)10(5s)2(5p)6(4f)10(6s)2⏟likely (30 electrons)

30 electrons which fill all orbits from4d10 to6s2 are likely there.

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Most popular questions from this chapter

(a) Figure out the electron configurations (in the notation of Equation

5.33) for the first two rows of the Periodic Table (up to neon), and check your

results against Table 5.1.

1s22s22p2(5.33).

(b) Figure out the corresponding total angular momenta, in the notation of

Equation 5.34, for the first four elements. List all the possibilities for boron,

carbon, and nitrogen.

LJ2S+1 (5.34).

Find the energy at the bottom of the first allowed band, for the caseβ=10 , correct to three significant digits. For the sake of argument, assume αa=1eV.

Derive the Stefan-Boltzmann formula for the total energy density in blackbody radiation

EV=(π2kB415ħ3C3)T4=7.57×10-16Jm-3K-4T4

Suppose you have three particles, and three distinct one-particle stateΨaX,ΨbX,andΨcxare available. How many different three-particle states can be constructed (a) if they are distinguishable particles, (b) if they are identical bosons, (c) if they are identical fermions? (The particles need not be in different states -ΨaX1,ΨaX2Ψax3would be one possibility, if the particles are distinguishable.)

Evaluate the integrals (Equation5.108 and 5.109) for the case of identical fermions at absolute zero. Compare your results with equations 5.43 and5.45. (Note for electrons there is an extra factor of 2 in Equations 5.108 and 5.109. to account for the spin degeneracy.)
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