Problem

Estimate Kα characteristic X-ray wavelengths: A hole. has already been produced in the n =...

Estimate Kα characteristic X-ray wavelengths: A hole. has already been produced in the n = 1 shell, and an n = 2 electron is poised to jump in. Assume that the electron behaves as though in a "hydrogenlike" atom (see Section 7.8), with energy given by Z2eff(-13.6eV/n2). Before the jump, it orbits Z protons, one remaining n = 1 electron, and (on average) half its seven fellow n = 2 electrons, for a Z2eff of Z - 4.5. After the jump, it orbits Z protons and half of its fellow n = 1 electron, for a Z2eff of Z - 0.5, Obtain a formula for 1/λ versus Z. Compare the predictions of this model with the experimental data given in Figure 8.19 and Table 8,4.

TABLE 8.4

Kα X-rays

Z

λ-1(nm-1)

20(Ca)

3.0

30(zn)

7.0

40(zr)

12.7

50(sn)

20.3

60(sn)

29.9

70(Yb)

41.8

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