Referring to Figure10.36, we see that the atomic number Z is proportional to f^1/2 or that Z² is proportional to f. Because the frequency of the characteristic x-ray lines is itself proportional to the energy of the associated x-ray photon, we are led to conclude that DE and hence the energies of the atomic levels also scale as Z². Based on this analysis (and ignoring any differences from the masses of their nuclei), how much greater is the energy associated with the ground state of helium (Z = 2) than that of hydrogen (Z = 1)?

Figure 10.36

Make a similar comparison between the ground state energies for sodium (Z = 11) and hydrogen.

Transcribed Image Text:

√fx 10³ (Hz¹/2) 48 42 36 30 24 18 12 6 0 T 1 1 T I T L 10 1 20 1 30 40 50 60 Atomic number (Z) L 70 1 80 KB Ka 1 90 100