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Chapter 8: Q56E (page 342)

Determine the rank according to increasing wavelength ofkα,kβ andLα.

Short Answer

Expert verified

The ranking of the spectral lines from lowest to highest is Kβ,Kα and Lα.

Step by step solution

01

 Step 1: Given data

The given data spectral lines Kβ,Kα andLα .

02

 Step 2: Concept of Energy

The energy E of the emitted ray is inversely proportional to the wavelength λ:

E~1λ

03

Determine the electronic configuration

The Kα line corresponds to the transition from n=2 to n=1.

The Kβ line corresponds to the transition from n=3 to n=1.

The Lα line corresponds to the transition from n=3 to n=2.

The energy E of the emitted ray is inversely proportional to the wavelengthλ , E~1λ.

We know that with increasing n , the energy difference ΔE becomes smaller.

Thus, the highest energy of the photon corresponds to the Kβ line.

The next one is the Kα line and the last one is the Lα line. In terms of the wavelength, we can rank the wavelengths from smallest to greatest as, λKβ<λKα<λLα.

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Most popular questions from this chapter

Slater Determinant: A convenient and compact way of expressing multi-particle states of anti-symmetric character for many fermions is the Slater determinant:

|ψn1x1m31ψn2x1m32ψn3x1m33···ψnNx1msNψn1x2m11ψn2x2m32ψn3x2m33···ψψn1x2msNψn3x3m31ψn2x3m12ψn3x3m33ψnNx3msN···············ψn1xNm11ψn2xNm32ψn3xNm33···ψnNxNmsN|

It is based on the fact that for N fermions there must be Ndifferent individual-particle states, or sets of quantum numbers. The ith state has spatial quantum numbers (which might be ni,ℓi, and mfi) represented simply byni and spin quantum number msi. Were it occupied by the ith particle, the slate would beψni(xj)msi a column corresponds to a given state and a row to a given particle. For instance, the first column corresponds to individual particle state ψn(xj)ms1. Where jprogresses (through the rows) from particle 1 to particle N. The first row corresponds to particle I. which successively occupies all individual-particle states (progressing through the columns). (a) What property of determinants ensures that the multiparticle state is 0 if any two individual particle states are identical? (b) What property of determinants ensures that switching the labels on any two particles switches the sign of the multiparticle state?

Were it to follow the standard pattern, what would be the electronic configuration of element 119.

Question:Figure 8.16 shows that in the Z = 3 to 10 filling of the n = 2 shell (lithium to neon), there is an upward trend in elements' first Ionization energies. Why is there a drop as Z goes from 4 to 5, from beryllium to boron?

As is done for helium in Table 8.3, determine for a carbon atom the various states allowed according to LS coupling. The coupling is between carbon's two 2p electrons (its filled 2s subshell not participating), one or which always remains in the 2p state. Consider cases in which the other is as high as the 3d level. (Note: Well both electrons are in the 2p, the exclusion principle restricts the number of states. The only allowed states are those in whichandlT are both even or both odd).

Your friends ask: “Why is there an exclusion principle?” Explain in the simplest terms.
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