Ɇɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ
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ɬ. ɟ. ɦɚɫɫɚ ɝɪɚɧɢɰɵ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɟɟ ɬɨɥɳɢɧɟ. ɉɨɫɤɨɥɶɤɭ ɝɪɚɧɢɰɚ ɨɛɥɚɞɚɟɬ ɢɧɟɪɰɢɟɣ, ɬɨ ɩɨɫɥɟ ɜɤɥɸɱɟɧɢɹ
ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɧɚ ɜɧɚɱɚɥɟ ɞɜɢɠɟɬɫɹ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɭɫɤɨɪɟɧɢɟɦ. ȿɟ ɫɤɨɪɨɫɬɶ ɧɟ ɦɨɠɟɬ ɧɟɨɝɪɚɧɢɱɟɧɧɨ ɜɨɡɪɚɫɬɚɬɶ, ɬɚɤ ɤɚɤ ɫ ɩɪɟɰɟɫɫɢɟɣ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɫɜɹɡɚɧɨ ɡɚɬɭɯɚɧɢɟ, ɩɪɢɜɨɞɹɳɟɟ ɤ ɬɨɪɦɨɠɟɧɢɸ ɞɜɢɠɟɧɢɹ ɝɪɚɧɢɰɵ. ɉɨ ɢɫɬɟɱɟɧɢɢ ɧɟɤɨɬɨɪɨɝɨ ɜɪɟɦɟɧɢ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɫɬɚɰɢɨɧɚɪɧɨɟ ɫɨɫɬɨɹɧɢɟ, ɬɚɤ ɱɬɨ ɷɧɟɪɝɢɹ, ɚ ɡɧɚɱɢɬ, ɢ ɫɤɨɪɨɫɬɶ ɞɜɢɠɭɳɟɣɫɹ ɝɪɚɧɢɰɵ ɨɫɬɚɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ. ɂɫɯɨɞɹ ɢɡ ɭɪɚɜɧɟɧɢɹ Ʌɚɧɞɚɭ–Ʌɢɮɲɢɰɚ (4.46), ɫ ɭɱɟɬɨɦ (4.55) ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɇɯ << ɇɷɮ ɞɥɹ ɷɧɟɪɝɢɢ, ɬɟɪɹɟɦɨɣ ɟɞɢɧɢɰɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɝɪɚɧɢɰɵ, ɛɭɞɟɬ ɫɩɪɚɜɟɞɥɢɜɨ ɜɵɪɚɠɟɧɢɟ
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ɇɷɮɆ dz § ȝ0ĮȖɆ ³ ɇɷɮ2 dz = 8ʌĮȖȝ0ɆǻȖɝɪ = ȕv2, |
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ɬ. ɟ. ɞɜɢɠɟɧɢɟ ɝɪɚɧɢɰɵ ɬɨɪɦɨɡɢɬɫɹ ɷɮɮɟɤɬɢɜɧɨɣ ɫɢɥɨɣ ȕv. |
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Ɍɨɪɦɨɠɟɧɢɟ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɜɹɡɤɨɫɬɢ: |
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DɆ · |
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ȕ = 4ʌĮȖȝ0Ɇmɝɪ = ¨ |
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³ ¨ |
¸ dz , |
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ɤɨɬɨɪɵɣ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɩɨɫɬɨɹɧɧɨɣ ɡɚɬɭɯɚɧɢɹ ɩɪɟɰɟɫɫɢɨɧɧɨɝɨ ɞɜɢɠɟɧɢɹ Į ɜ ɭɪɚɜɧɟɧɢɢ Ʌɚɧɞɚɭ–Ʌɢɮɲɢɰɚ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɜɹɡɤɨɫɬɢ – ɜɚɠɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜɟɳɟɫɬɜɚ. Ɉɧ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɚɤɬɨɪɚɦɢ, ɫɯɨɞɧɵɦɢ ɫ ɩɪɢɱɢɧɚɦɢ ɡɚɬɭɯɚɧɢɹ ɩɪɢ ɩɪɟɰɟɫɫɢɨɧɧɨɦ ɞɜɢɠɟɧɢɢ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɢ ɮɟɪɪɨɦɚɝɧɢɬɧɨɦ ɪɟɡɨɧɚɧɫɟ. ɍ ɜɟɳɟɫɬɜ ɫɨ ɡɧɚɱɢɬɟɥɶɧɨɣ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶɸ ɜɤɥɚɞ ɜ ɡɚɬɭɯɚɧɢɟ ɞɚɸɬ ɬɚɤɠɟ ɦɢɤɪɨɜɢɯɪɟɜɵɟ ɬɨɤɢ, ɜɨɡɧɢɤɚɸɳɢɟ ɩɪɢ ɞɜɢɠɟɧɢɢ ɝɪɚɧɢɰɵ. Ɍɚɤɨɣ ɜɤɥɚɞ ɦɨɠɟɬ ɛɵɬɶ ɨɱɟɧɶ ɡɧɚɱɢɬɟɥɶɧɵɦ. ȼ ɦɟɬɚɥɥɢɱɟɫɤɢɯ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚɯ ɡɚɬɭɯɚɧɢɟ ɞɜɢɠɟɧɢɹ ɝɪɚɧɢɰ ɩɪɚɤɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɜɢɯɪɟɜɵɦɢ ɬɨɤɚɦɢ, ɚ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɨɤɫɢɞɧɵɯ ɦɚɬɟɪɢɚɥɨɜ (ɮɟɪɪɢɬɨɜ) ɜɥɢɹɧɢɟɦ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ.
141
ȼ ɫɥɚɛɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ, ɤɨɝɞɚ ɝɪɚɧɢɰɚ ɫɦɟɳɚɟɬɫɹ ɧɚ ɦɚɥɵɟ ɪɚɫɫɬɨɹɧɢɹ ɜ ɩɪɟɞɟɥɚɯ ɩɟɪɜɨɣ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɹɦɵ, ɟɟ ɫɤɨɪɨɫɬɶ ɧɟɥɶɡɹ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɨɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɨɹɜɥɹɸɬɫɹ ɢɧɟɪɰɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ ɝɪɚɧɢɰɵ ɢ ɟɟ ɫɦɟɳɟɧɢɹ ɧɨɫɹɬ ɜɹɡɤɢɣ ɯɚɪɚɤɬɟɪ. ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɝɪɚɧɢɰɵ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ
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ɱɬɨ ɮɨɪɦɚɥɶɧɨ ɫɨɜɩɚɞɚɟɬ ɫ ɭɪɚɜɧɟɧɢɟɦ ɜɵɧɭɠɞɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɝɚɪɦɨɧɢɱɟɫɤɨɝɨ ɨɫɰɢɥɥɹɬɨɪɚ. ȿɫɥɢ ɩɪɢɥɨɠɟɧɨ ɩɟɪɟɦɟɧɧɨɟ ɦɚɝɧɢɬ-
ɧɨɟ ɩɨɥɟ ɇɯ = ɇɯ |
exp(jȦt), ɬɨ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (4.59) ɢɦɟɟɬ ɜɢɞ |
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ȼɤɥɚɞ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɝɪɚɧɢɰɵ ɜ ɦɚɝɧɢɬɧɭɸ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɪɚɜɟɧ 2zɆS /Hx, ɬɚɤ ɱɬɨ ɩɪɢ ɩɚɪɚɥɥɟɥɶɧɨɦ ɪɚɫɩɨɥɨɠɟɧɢɢ 180º-ɯ
ɝɪɚɧɢɰ ɧɚ ɪɚɫɫɬɨɹɧɢɢ d ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɩɨɥɭɱɚɟɦ ɜɵɪɚɠɟɧɢɟ
Ȥ(Ȧ) = Ȥ |
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ɝɞɟ Ȥɫɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ (4.51). |
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ȼɨɫɩɪɢɢɦɱɢɜɨɫɬɶ, |
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ɯɚɪɚɤɬɟɪ: F F jF . |
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ȿɫɥɢ ɨɛɨɡɧɚɱɢɬɶ |
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ɱɚɫɬɨɬɭ ɪɟɡɨɧɚɧɫɚ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ, ɚ |
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ɱɚɫɬɨɬɭ ɪɟɥɚɤɫɚɰɢɢ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ ɢ ɜɵɞɟɥɢɬɶ ɞɟɣɫɬɜɢɬɟɥɶɧɭɸ ɢ ɦɧɢɦɭɸ ɱɚɫɬɢ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ, ɬɨ ɩɨɥɭɱɢɦ:
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142
Fcc = Ȥɫɦ |
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ȿɫɥɢ ɡɚɬɭɯɚɧɢɟ ɫɥɚɛɨɟ, ɬ. ɟ. ȕ2 << k |
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ɬɨɬɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɢɦɟɟɬ ɪɟɡɨɧɚɧɫɧɵɣ ɯɚɪɚɤɬɟɪ, ɩɨɯɨɠɢɣ ɧɚ ɤɪɢɜɵɟ ɪɢɫ. 4.17, ɚ. ȼ ɫɥɭɱɚɟ ɫɢɥɶɧɨɝɨ ɡɚɬɭɯɚɧɢɹ (Ȧ0 >> Ȧɪɟɥ) ɜɵɪɚɠɟɧɢɹ (4.64) ɢ (4.65) ɩɪɟɨɛɪɚɡɭɸɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
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ɢ ɱɚɫɬɨɬɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɢɦɟɟɬ ɪɟɥɚɤɫɚɰɢɨɧɧɵɣ ɯɚɪɚɤɬɟɪ (ɫɦ.
ɪɢɫ. 4.17, ɛ).
ɑɚɫɬɨɬɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ/ɩɪɨɧɢɰɚɟɦɨɫɬɢ (ɟɟ ɟɳɟ ɧɚɡɵɜɚɸɬ ɦɚɝɧɢɬɧɵɦ ɫɩɟɤɬɪɨɦ) ɪɟɥɚɤɫɚɰɢɨɧɧɨɝɨ ɜɢɞɚ ɧɚɢɛɨɥɟɟ ɹɪɤɨ ɩɪɨɹɜɥɹɟɬɫɹ ɞɚɠɟ ɜ ɨɤɫɢɞɧɵɯ ɦɚɬɟɪɢɚɥɚɯ ɫ ɜɵɫɨɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ. ɇɚ ɪɢɫ. 4.19 ɩɨɤɚɡɚɧɚ ɞɚɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɞɥɹ Fe3O4 (ɦɚɝɧɟɬɢɬɚ).
Ɋɢɫ. 4.19. ɑɚɫɬɨɬɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɫɨɫɬɚɜɥɹɸɳɢɯ ɦɚɝɧɢɬɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɦɨɧɨɤɪɢɫɬɚɥɥɚ ɦɚɝɧɟɬɢɬɚ (ȕ § 0,5)
143
ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɞɢɫɩɟɪɫɢɹ ɦɚɝɧɢɬɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɮɟɪɪɢɬɨɜ ɢɦɟɟɬ ɪɟɡɨɧɚɧɫɧɵɣ ɯɚɪɚɤɬɟɪ (ɪɢɫ. 4.20), ɯɨɬɹ ɟɟ ɜɢɞ ɹɜɥɹɟɬɫɹ ɛɨɥɟɟ ɫɥɨɠɧɵɦ, ɱɟɦ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 4.17, ɚ.
Ɋɢɫ. 4.20. Ɇɚɝɧɢɬɧɵɟ ɫɩɟɤɬɪɵ ɩɨɥɢɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯ Ni–Zn-ɮɟɪɪɢɬɨɜ
Ⱦɟɥɨ ɜ ɬɨɦ, ɱɬɨ ɪɟɚɥɶɧɵɣ ɮɟɪɪɨɦɚɝɧɟɬɢɤ ɫɨɞɟɪɠɢɬ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ, ɩɚɪɚɦɟɬɪɵ ɤɨɬɨɪɵɯ (kɝɪ, mɝɪ, ȕ) ɦɨɝɭɬ
ɨɬɥɢɱɚɬɶɫɹ. ɉɪɢ ɷɬɨɦ ɪɚɡɧɵɟ ɞɨɦɟɧɧɵɟ ɝɪɚɧɢɰɵ ɦɨɝɭɬ ɜɧɨɫɢɬɶ ɪɚɡɧɵɟ ɜɤɥɚɞɵ ɜ ɫɭɦɦɚɪɧɭɸ ɜɟɥɢɱɢɧɭ Ȥ ɢ ɨɬɥɢɱɚɬɶɫɹ ɫɨɛɫɬɜɟɧɧɵɦɢ ɱɚɫɬɨɬɚɦɢ ɪɟɡɨɧɚɧɫɚ ɢ ɪɟɥɚɤɫɚɰɢɢ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɲɢɪɟɧɢɸ ɨɛɥɚɫɬɢ ɞɢɫɩɟɪɫɢɢ ɢ ɢɡɦɟɧɟɧɢɸ ɜɢɞɚ ɤɪɢɜɵɯ ɞɢɫɩɟɪɫɢɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɬɟɨɪɟɬɢɱɟɫɤɢɦɢ ɡɚɜɢɫɢɦɨɫɬɹɦɢ, ɜɵɜɟɞɟɧɧɵɦɢ ɞɥɹ ɢɞɟɚɥɢɡɢɪɨɜɚɧɧɨɝɨ ɫɥɭɱɚɹ ɨɞɧɨɣ ɞɨɦɟɧɧɨɣ ɝɪɚɧɢɰɵ. Ʉɪɢɜɵɟ, ɩɨɤɚɡɚɧɧɵɟ ɧɚ ɪɢɫ. 4.20, ɞɟɦɨɧɫɬɪɢɪɭɸɬ ɦɚɝɧɢɬɧɵɟ ɫɩɟɤɬɪɵ, ɜɢɞ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɨɛɴɹɫɧɢɬɶ ɧɚ ɨɫɧɨɜɟ ɜɵɲɟɩɪɢɜɟɞɟɧɧɵɯ ɪɚɫɫɭɠɞɟɧɢɣ.
Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɩɪɢɜɟɞɟɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ, ɞɢɧɚɦɢɱɟɫɤɨɟ ɩɨɜɟɞɟɧɢɟ ɜ ɩɟɪɟɦɟɧɧɨɦ ɩɨɥɟ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ (ɩɪɨɰɟɫɫɵ ɜɪɚ-
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ɳɟɧɢɹ) ɢ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ (ɩɪɨɰɟɫɫɵ ɫɦɟɳɟɧɢɹ) ɞɟɦɨɧɫɬɪɢɪɭɟɬ ɪɟɡɨɧɚɧɫɧɵɣ (ɪɟɠɟ ɪɟɥɚɤɫɚɰɢɨɧɧɵɣ) ɯɚɪɚɤɬɟɪ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɭɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ, ɤɚɤ ɩɪɚɜɢɥɨ, ɱɚɫɬɨɬɵ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɪɟɡɨɧɚɧɫɚ ɢɦɟɸɬ ɡɧɚɱɟɧɢɹ ɧɚ ɩɨɪɹɞɨɤ (ɩɨɪɹɞɤɢ) ɛɨɥɶɲɟ, ɱɟɦ ɱɚɫɬɨɬɵ ɪɟɡɨɧɚɧɫɚ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ. ɉɨɷɬɨɦɭ ɱɚɫɬɨɬɧɵɟ ɨɛɥɚɫɬɢ, ɜ ɤɨɬɨɪɵɯ ɩɪɨɹɜɥɹɟɬɫɹ ɬɨɬ ɢɥɢ ɢɧɨɣ ɩɪɨɰɟɫɫ, ɤɚɤ ɩɪɚɜɢɥɨ, ɞɚɥɟɤɨ ɪɚɡɧɟɫɟɧɵ ɩɨ ɱɚɫɬɨɬɧɨɦɭ ɞɢɚɩɚɡɨɧɭ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɧɚ ɪɢɫ. 4.21 ɩɨɤɚɡɚɧ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɣ ɦɚɝɧɢɬɧɵɣ ɫɩɟɤɬɪ ɦɚɝɧɢɟɜɨɝɨ ɮɟɪɪɢɬɚ ɜ ɲɢɪɨɤɨɦ ɞɢɚɩɚɡɨɧɟ ɱɚɫɬɨɬ. ȼ ɧɟɦ ɱɟɬɤɨ ɩɪɨɫɦɚɬɪɢɜɚɸɬɫɹ ɞɜɟ ɨɛɥɚɫɬɢ ɞɢɫɩɟɪɫɢɢ ɦɚɝɧɢɬɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ: «ɧɢɡɤɨɱɚɫɬɨɬɧɚɹ» – ɫ ɱɚɫɬɨɬɨɣ ɪɟɡɨɧɚɧɫɚ ~50 ɆȽɰ ɢ «ɜɵɫɨɤɨɱɚɫɬɨɬɧɚɹ» – ɫ ɱɚɫɬɨɬɨɣ ɪɟɡɨɧɚɧɫɚ ɱɭɬɶ ɜɵɲɟ 1000 ɆȽɰ. ɇɢɡɤɨɱɚɫɬɨɬɧɵɣ ɩɪɨɰɟɫɫ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɤ ɫɦɟɳɟɧɢɸ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ, ɚ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɣ – ɤ ɜɪɚɳɟɧɢɸ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ.
Ɋɢɫ. 4.21. Ɇɚɝɧɢɬɧɵɣ ɫɩɟɤɬɪ ɦɚɝɧɢɟɜɨɝɨ ɮɟɪɪɢɬɚ
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ɂɡ ɤɪɢɜɵɯ ɪɢɫ. 4.20 ɫɥɟɞɭɟɬ ɟɳɟ ɨɞɧɚ ɜɚɠɧɚɹ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ: ɱɟɦ ɛɨɥɶɲɟ ɡɧɚɱɟɧɢɟ ɧɚɱɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ, ɬɟɦ ɩɪɢ ɛɨɥɟɟ ɧɢɡɤɢɯ ɱɚɫɬɨɬɚɯ ɧɚɱɢɧɚɸɬɫɹ ɟɟ ɱɚɫɬɨɬɧɵɟ ɢɡɦɟɧɟɧɢɹ. ɉɪɢɱɢɧɚɦɢ ɬɚɤɨɣ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ (ɞɥɹ ɩɪɨɰɟɫɫɚ ɫɦɟɳɟɧɢɹ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ) ɹɜɥɹɟɬɫɹ ɬɟɫɧɚɹ ɫɜɹɡɶ ɩɚɪɚɦɟɬɪɨɜ ɝɪɚɧɢɰɵ, ɜɯɨɞɹɳɢɯ ɜ ɭɪɚɜɧɟɧɢɟ ɟɟ ɞɜɢɠɟɧɢɹ, ɫ ɜɟɥɢɱɢɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɢ ɫɨɛɫɬɜɟɧɧɵɦɢ ɱɚɫɬɨɬɚɦɢ ɟɟ ɤɨɥɟɛɚɧɢɣ (ɫɦ. (4.51), (4.62), (4.63)).
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ ɤ ɝɥɚɜɟ 4
1.Ʉɚɤ ɩɨɥɭɱɢɬɶ ɪɚɡɦɚɝɧɢɱɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɨɛɪɚɡɰɚ?
2.Ʉɚɤɢɟ ɩɚɪɚɦɟɬɪɵ ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɨɫɧɨɜɧɭɸ ɤɪɢɜɭɸ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɢ ɩɟɬɥɸ ɝɢɫɬɟɪɟɡɢɫɚ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ?
3.Ɉɛɴɹɫɧɢɬɟ ɩɪɢɪɨɞɭ «ɫɤɚɱɤɨɜ Ȼɚɪɤɝɚɭɡɟɧɚ».
4.Ʉɚɤɨɜɵ ɦɟɯɚɧɢɡɦɵ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɨɛɪɚɡɰɚ? ȼ ɱɟɦ ɢɯ ɫɯɨɞɫɬɜɨ ɢ ɪɚɡɥɢɱɢɟ?
5.ɉɪɢ ɤɚɤɢɯ ɭɫɥɨɜɢɹɯ ɩɪɨɰɟɫɫ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɹ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɨɛɪɚɡɰɚ ɛɭɞɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɫ ɩɪɟɨɛɥɚɞɚɧɢɟɦ ɦɟɯɚɧɢɡɦɚ ɜɪɚɳɟɧɢɹɜɟɤɬɨɪɚɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢɢɥɢ ɫɦɟɳɟɧɢɹɞɨɦɟɧɧɵɯɝɪɚɧɢɰ?
6.Ʉɚɤɨɜɵ ɜɨɡɦɨɠɧɵɟ ɦɟɯɚɧɢɡɦɵ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɤɨɷɪɰɢɬɢɜɧɨɣ ɫɢɥɵ ɜ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚɯ?
7.ȼ ɱɟɦ ɡɚɤɥɸɱɚɟɬɫɹ ɨɫɧɨɜɧɚɹ ɩɪɢɱɢɧɚ ɩɨɬɟɪɶ ɧɚ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɟ ɞɥɹ ɦɚɬɟɪɢɚɥɨɜ, ɨɛɥɚɞɚɸɳɢɯ ɜɵɫɨɤɢɦ ɢ ɧɢɡɤɢɦ ɭɞɟɥɶɧɵɦ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ?
8.ɉɨɱɟɦɭ ɡɚɜɢɫɢɦɨɫɬɢ ɧɚɱɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ (ɩɪɢ ɫɥɚɛɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ) ɢɦɟɸɬ ɜɢɞ ɤɪɢɜɵɯ ɫ ɦɚɤɫɢɦɭɦɨɦ?
9.Ɇɨɠɟɬ ɥɢ ɨɞɢɧ ɦɚɬɟɪɢɚɥ ɢɦɟɬɶ ɧɟɫɤɨɥɶɤɨ ɪɚɡɧɵɯ ɱɚɫɬɨɬ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɮɟɪɪɨɦɚɝɧɢɬɧɨɝɨ ɪɟɡɨɧɚɧɫɚ?
10.ɑɟɦ ɨɛɭɫɥɨɜɥɟɧɚ ɫɥɨɠɧɚɹ ɮɨɪɦɚ ɦɚɝɧɢɬɧɵɯ ɫɩɟɤɬɪɨɜ ɮɟɪ-
ɪɢɬɨɜ?
11.Ʉɚɤɚɹ ɫɜɹɡɶ ɫɭɳɟɫɬɜɭɟɬ ɦɟɠɞɭ ɡɧɚɱɟɧɢɟɦ ɧɚɱɚɥɶɧɨɣ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ (ɩɪɨɧɢɰɚɟɦɨɫɬɢ) ɮɟɪɪɢɬɚ ɢ ɩɨɥɨɠɟɧɢɟɦ ɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɫɩɟɤɬɪɚ ɧɚ ɱɚɫɬɨɬɧɨɣ ɨɫɢ ɜ ɫɥɭɱɚɹɯ: 1) ɩɪɟɨɛɥɚɞɚɧɢɹ ɩɪɨɰɟɫɫɚ ɜɪɚɳɟɧɢɹ ɜɟɤɬɨɪɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ, 2) ɩɪɟɨɛɥɚɞɚɧɢɹ ɩɪɨɰɟɫɫɚ ɫɦɟɳɟɧɢɹ ɞɨɦɟɧɧɵɯ ɝɪɚɧɢɰ?
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Ƚɥɚɜɚ 5. ɆȺȽɇɂɌɇɕȿ ɊȿɁɈɇȺɇɋɇɕȿ ɗɎɎȿɄɌɕ ɂ ɂɏ ɂɋɉɈɅɖɁɈȼȺɇɂȿ
Ɉɛɳɢɦ ɬɟɪɦɢɧɨɦ «ɦɚɝɧɢɬɧɵɟ ɪɟɡɨɧɚɧɫɧɵɟ ɷɮɮɟɤɬɵ» ɨɛɨɡɧɚɱɚɸɬ ɢɡɛɢɪɚɬɟɥɶɧɨɟ ɩɨɝɥɨɳɟɧɢɟ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ (ɤɚɤ ɩɪɚɜɢɥɨ, ɩɟɪɟɦɟɧɧɨɝɨ) ɷɥɟɤɬɪɨɧɧɨɣ ɢɥɢ ɹɞɟɪɧɨɣ ɩɨɞɫɢɫɬɟɦɨɣ ɜɟɳɟɫɬɜɚ, ɩɨɞɜɟɪɝɧɭɬɨɝɨ ɜɨɡɞɟɣɫɬɜɢɸ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ɇɟɯɚɧɢɡɦ ɬɚɤɨɝɨ ɩɨɝɥɨɳɟɧɢɹ ɫɜɹɡɚɧ ɫ ɤɜɚɧɬɨɜɵɦɢ ɩɟɪɟɯɨɞɚɦɢ ɜ ɷɬɢɯ ɩɨɞɫɢɫɬɟɦɚɯ ɦɟɠɞɭ ɞɢɫɤɪɟɬɧɵɦɢ ɭɪɨɜɧɹɦɢ ɷɧɟɪɝɢɢ, ɜɨɡɧɢɤɚɸɳɢɦɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɫɬɨɹɧɧɨɝɨ ɩɨɥɹ. Ɍɚɤɢɟ ɭɪɨɜɧɢ ɱɚɳɟ ɜɫɟɝɨ ɨɛɭɫɥɨɜɥɟɧɵ ɤɜɚɧɬɨɜɚɧɢɟɦ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫɩɢɧɨɜɵɯ ɢ ɨɪɛɢɬɚɥɶɧɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ (ɡɟɟɦɚɧɨɜɫɤɢɟ ɭɪɨɜɧɢ). Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ ɜ ɦɚɝɧɢɬɧɵɯ ɪɟɡɨɧɚɧɫɚɯ ɨɩɪɟɞɟɥɹɸɬɫɹ ɪɚɡɥɢɱɧɵɦɢ ɜɢɞɚɦɢ ɜɧɭɬɪɟɧɧɢɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɧɚ ɚɬɨɦɧɨɦ ɢ ɦɨɥɟɤɭɥɹɪɧɨɦ ɭɪɨɜɧɹɯ ɢ ɜ ɜɟɳɟɫɬɜɚɯ ɜ ɰɟɥɨɦ. Ɋɟɡɨɧɚɧɫɧɵɟ ɩɪɨɰɟɫɫɵ ɜ ɦɚɝɧɢɬɨɭɩɨɪɹɞɨɱɟɧɧɵɯ ɜɟɳɟɫɬɜɚɯ (ɮɟɪɪɨ-, ɮɟɪɪɢ-, ɚɧɬɢɮɟɪɪɨɦɚɝɧɟɬɢɤɢ) ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɩɪɨɰɟɫɫɨɜ ɜ ɜɟɳɟɫɬɜɚɯ, ɧɟ ɨɛɥɚɞɚɸɳɢɯ ɚɬɨɦɧɵɦ ɦɚɝɧɢɬɧɵɦ ɩɨɪɹɞɤɨɦ (ɞɢɚ-, ɩɚɪɚɦɚɝɧɟɬɢɤɢ), ɩɨɫɤɨɥɶɤɭ, ɧɚɩɪɢɦɟɪ, ɜ ɩɚɪɚɦɚɝɧɟɬɢɤɚɯ ɪɟɡɨɧɚɧɫɧɨɟ ɩɨɝɥɨɳɟɧɢɟ ɜɨɡɧɢɤɚɟɬ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬɞɟɥɶɧɵɯ ɚɬɨɦɨɜ ɢɡ ɨɞɧɨɝɨ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ ɞɪɭɝɨɟ, ɚ ɜ ɦɚɝɧɢɬɨɭɩɨɪɹɞɨɱɟɧɧɵɯ ɜɟɳɟɫɬɜɚɯ ɧɚɛɥɸɞɚɟɬɫɹ ɪɟɡɨɧɚɧɫɧɨɟ ɩɨɝɥɨɳɟɧɢɟ ɦɚɝɧɢɬɧɨɣ ɫɢɫɬɟɦɨɣ ɜ ɰɟɥɨɦ.
5.1. Ɇɚɝɧɢɬɧɵɟ ɫɜɨɣɫɬɜɚ ɚɬɨɦɧɵɯ ɹɞɟɪ
ɇɭɤɥɨɧɵ (ɩɪɨɬɨɧɵ ɢ ɧɟɣɬɪɨɧɵ) ɢ ɫɨɫɬɨɹɳɢɟ ɢɡ ɧɢɯ ɚɬɨɦɧɵɟ ɹɞɪɚ ɨɛɥɚɞɚɸɬ ɫɨɛɫɬɜɟɧɧɵɦɢ ɦɚɝɧɢɬɧɵɦɢ ɦɨɦɟɧɬɚɦɢ, ɤɨɬɨɪɵɟ ɨɛɭɫɥɨɜɥɢɜɚɸɬ ɹɞɟɪɧɵɣ ɦɚɝɧɟɬɢɡɦ. Ʉɚɡɚɥɨɫɶ ɛɵ, ɩɪɨɬɨɧ ɤɚɤ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɚɹ ɱɚɫɬɢɰɚ ɞɨɥɠɟɧ ɨɛɥɚɞɚɬɶ ɧɚɦɧɨɝɨ ɦɟɧɶɲɢɦɫɩɢɧɨɜɵɦ ɦɚɝɧɢɬɧɵɦ ɦɨɦɟɧɬɨɦ, ɱɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɦɨɦɟɧɬ ɷɥɟɤɬɪɨɧɚ, ɢɡ-ɡɚ ɫɭɳɟɫɬɜɟɧɧɨɣ ɪɚɡɧɢɰɵ ɜ ɦɚɫɫɟ*. Ɍɟɨɪɟɬɢɱɟɫɤɢ, ɡɧɚɱɟɧɢɟ ɹɞɟɪɧɨɝɨ ɦɚɝɧɟɬɨɧɚ ɞɨɥɠɧɨ ɪɚɜɧɹɬɶɫɹ:
ȝɹɞ = 2ɟɆ= = 1836PB = 5,051 · 10–27 Ⱥ · ɦ2.
ɇɟɣɬɪɨɧ ɤɚɤ ɱɚɫɬɢɰɚ, ɧɟ ɨɛɥɚɞɚɸɳɚɹ ɡɚɪɹɞɨɦ, ɧɟ ɞɨɥɠɟɧ ɛɵɥ ɛɵ ɨɛɥɚɞɚɬɶ ɢ ɦɚɝɧɢɬɧɵɦ ɦɨɦɟɧɬɨɦ.
* Ɇɚɫɫɚ ɩɪɨɬɨɧɚ Ɇ ɜ 1836 ɪɚɡ ɛɨɥɶɲɟ ɦɚɫɫɵ ɷɥɟɤɬɪɨɧɚ.
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ȼ ɪɟɚɥɶɧɨɫɬɢ ɠɟ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɩɪɨɬɨɧɚ ȝɪ § 2,79ȝɹɞ, ɚ ɧɟɣɬɪɨɧ ɬɚɤɠɟ ɢɦɟɟɬ ɫɨɛɫɬɜɟɧɧɵɣ ɦɚɝɧɢɬɧɵɣ ɦɨ-
ɦɟɧɬ ȝn § 1,91 ȝɹɞ. ɋɨɜɪɟɦɟɧɧɚɹ ɤɜɚɧɬɨɜɚɹ ɬɟɨɪɢɹ ɧɭɤɥɨɧɨɜ ɧɟ ɞɚɟɬ
ɞɟɬɚɥɶɧɨɝɨ ɨɛɴɹɫɧɟɧɢɹ ɷɬɨɣ ɚɧɨɦɚɥɢɢ. ȼ ɨɬɥɢɱɢɟ ɨɬ ɷɥɟɤɬɪɨɧɧɵɯ ɦɨɦɟɧɬɨɜ, ɤɨɬɨɪɵɟ ɨɛɵɱɧɨ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɦɨɦɟɧɬɭ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɩɨ ɩɪɢɱɢɧɟ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ, ɹɞɟɪɧɵɟ ɦɨɦɟɧɬɵ ɨɛɵɱɧɨ ɩɨɥɨɠɢɬɟɥɶɧɵ.
ɉɨɞ ɫɩɢɧɨɦ ɹɞɪɚ I ɩɨɧɢɦɚɟɬɫɹ ɩɨɥɧɵɣ ɦɨɦɟɧɬ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ ɹɞɪɚ, ɪɚɜɧɵɣ ɜɟɤɬɨɪɧɨɣ ɫɭɦɦɟ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɫɨɫɬɚɜɥɹɸɳɢɯ ɟɝɨ ɧɭɤɥɨɧɨɜ ɢ ɢɯ ɫɩɢɧɨɜ. Ɉɪɛɢɬɚɥɶɧɵɟ ɦɨɦɟɧɬɵ ɧɭɤɥɨɧɨɜ ɜ ɟɞɢɧɢɰɚɯ ƫ ɜɵɪɚɠɚɸɬɫɹ ɰɟɥɵɦɢ ɱɢɫɥɚɦɢ, ɚ ɫɩɢɧɨɜɵɟ ɦɨɦɟɧɬɵ – ɩɨɥɭɰɟɥɵɦɢ (ɬ. ɟ. ɰɟɥɵɦɢ ɜ ɟɞɢɧɢɰɚɯ ƫ/2). Ɍɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ, ɱɬɨ ɭ ɹɞɟɪ ɫ ɱɟɬɧɵɦɢ Z (ɚɬɨɦɧɵɣ ɧɨɦɟɪ ɷɥɟɦɟɧɬɚ) ɢ A – Z (Ⱥ – ɚɬɨɦɧɚɹ ɦɚɫɫɚ ɷɥɟɦɟɧɬɚ) ɜɫɟɝɞɚ ɫɩɢɧ I = 0 ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ, ɨɛɭɫɥɨɜɥɟɧɨ ɫɩɟɰɢɮɢɤɨɣ ɹɞɟɪɧɵɯ ɫɢɥ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɜɫɟ ɹɞɪɚ ɫ I 0 ɢɦɟɸɬ ɢ ɧɟɧɭɥɟɜɨɣ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ.
ɂɡ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɩɨ ɫɩɢɧɚɦ ɢ ɦɚɝɧɢɬɧɵɦ ɦɨɦɟɧɬɚɦɚɬɨɦɧɵɯɹɞɟɪ ɦɨɠɧɨ ɫɞɟɥɚɬɶɫɥɟɞɭɸɳɢɟɨɛɳɢɟɜɵɜɨɞɵ:
1) ɜɫɟ ɹɞɪɚ ɫ ɱɟɬɧɵɦ ɱɢɫɥɨɦ ɩɪɨɬɨɧɨɜ ɢ ɧɟɣɬɪɨɧɨɜ (ɱɟɬɧɨɟ Z) ɨɛɥɚɞɚɸɬ ɧɭɥɟɜɵɦ ɫɩɢɧɨɦ;
2) ɹɞɪɚ ɫ ɧɟɱɟɬɧɵɦ A ɢ ɥɸɛɵɦ Z ɢɦɟɸɬ ɫɩɢɧ (n 1
2)=, ɝɞɟ n = 0, 1, 2, ... ;
3) ɹɞɪɚ ɫ ɧɟɱɟɬɧɵɦ Z ɢ ɧɟɱɟɬɧɵɦ (A – Z) (ɬ. ɟ. ɫ ɱɟɬɧɵɦ A) ɢɦɟɸɬ ɫɩɢɧ n=, ɝɞɟ n = 1, 2, 3, … .
Ɋɢɫ. 5.1. Ɋɚɫɳɟɩɥɟɧɢɟ ɹɞɟɪɧɵɯ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɪɨɜɧɟɣ 59Co (I = 7/2) ɜ ɫɜɟɪɯɬɨɧɤɨɦ ɩɨɥɟ
ɉɪɢ ɩɪɢɥɨɠɟɧɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɢɧɞɭɤɰɢɟɣ B0 ɜ ɧɚɩɪɚɜɥɟɧɢɢ Oz ɡɟɟɦɚɧɨɜɫɤɢ ɪɚɫɳɟɩɥɹɸɬɫɹ (2I + 1) ɦɚɝɧɢɬɧɵɯ ɭɪɨɜɧɟɣ (ɪɢɫ. 5.1), ɱɬɨ ɜɟɞɟɬ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɛɨɥɶɰɦɚɧɨɜɫɤɢɯ ɧɚɫɟɥɟɧɧɨɫɬɟɣ. ɇɟɛɨɥɶɲɚɹ ɤɨɧɟɱɧɚɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɢɧɞɭɰɢɪɭɟɬɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɨɥɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɤɨɧɨɦ Ʉɸɪɢ. ȼ ɩɨɥɟ 1 Ɍɥ ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɪɚɫɳɟɩɥɟɧɢɟ ɞɥɹ
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ɩɪɨɬɨɧɚ ɪɚɜɧɨ 2,8 · 10–26 Ⱦɠ. Ɋɚɡɧɢɰɚ ɜ ɡɚɫɟɥɟɧɧɨɫɬɢ ɞɜɭɯ ɭɪɨɜɧɟɣ ɦɟɧɶɲɟ, ɱɟɦ 1 ɱɚɫɬɢɰɚ ɧɚ 105 ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ.
Ɍɨɬ ɮɚɤɬ, ɱɬɨ ɞɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɚɬɨɦɧɵɯ ɹɞɟɪ ɫɩɢɧɵ ɧɟ ɩɪɟɜɵɲɚɸɬ 7/2, ɩɨɡɜɨɥɹɟɬ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ ɧɭɤɥɨɧɵ, ɩɨɞɨɛɧɨ ɷɥɟɤɬɪɨɧɚɦ ɚɬɨɦɧɨɣ ɨɛɨɥɨɱɤɢ, ɨɛɪɚɡɭɸɬ ɡɚɦɤɧɭɬɵɟ «ɫɥɨɢ», ɞɥɹ ɤɨɬɨɪɵɯ ɡɧɚɱɟɧɢɹ ɫɩɢɧɚ ɢ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɪɚɜɧɵ ɧɭɥɸ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɩɢɧ ɹɞɪɚ ɹɜɥɹɟɬɫɹ ɪɟɡɭɥɶɬɚɬɨɦ ɫɥɨɠɟɧɢɹ ɫɩɢɧɨɜ ɥɢɲɶ ɧɟɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɧɭɤɥɨɧɨɜ, ɧɟ ɜɨɲɟɞɲɢɯ ɜ ɡɚɦɤɧɭɬɵɟ ɫɥɨɢ. ɇɚɩɪɢ-
ɦɟɪ, ɜ ɹɞɪɚɯ He12 , Cl126 ɢ ɞɪɭɝɢɯ ɩɨɞɨɛɧɵɯ ɷɥɟɦɟɧɬɨɜ ɫ I = 0 ɜɫɟ ɧɭ-
ɤɥɨɧɵ ɜɯɨɞɹɬ ɜ ɡɚɦɤɧɭɬɵɟ ɫɥɨɢ. ȼ ɹɞɪɟ N147 ɲɟɫɬɶ ɧɟɣɬɪɨɧɨɜ ɢ
ɲɟɫɬɶ ɩɪɨɬɨɧɨɜ ɨɛɪɚɡɭɸɬ ɡɚɦɤɧɭɬɵɟ ɫɥɨɢ, ɚ ɫɟɞɶɦɵɟ ɧɟɣɬɪɨɧ ɢ ɩɪɨɬɨɧ ɞɚɸɬ ɪɟɡɭɥɶɬɢɪɭɸɳɢɣ ɫɩɢɧ ɹɞɪɚ, ɪɚɜɧɵɣ ɢɯ ɫɭɦɦɟ: I = 1. Ɉɞɧɚɤɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɷɬɨɝɨ ɹɞɪɚ ɧɟ ɪɚɜɟɧ, ɧɚɩɪɢɦɟɪ, ɦɚɝɧɢɬɧɨɦɭ ɦɨɦɟɧɬɭ ɞɟɣɬɪɨɧɚ, ɢɦɟɸɳɟɝɨ ɬɨɬ ɠɟ ɫɩɢɧ I.
ȼ ɫɥɭɱɚɟ ɛɨɥɟɟ ɬɹɠɟɥɵɯ ɹɞɟɪ ɷɧɟɪɝɢɢ ɫɩɢɧɨɜɵɯ ɤɜɚɧɬɨɜɵɯ ɱɢɫɟɥ ɦɨɝɭɬ ɞɨɫɬɢɝɚɬɶ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɣ. Ɉɛɴɹɫɧɟɧɢɟ ɦɚɝɧɢɬɧɵɯ ɫɜɨɣɫɬɜ ɚɬɨɦɧɵɯ ɹɞɟɪ ɜɨɡɦɨɠɧɨ ɧɚ ɨɫɧɨɜɟ ɨɛɨɥɨɱɟɱɧɨɣ ɦɨɞɟɥɢ. ȼ ɫɥɭɱɚɟ ɫɪɟɞɧɢɯ ɢ ɬɹɠɟɥɵɯ ɹɞɟɪ, ɧɚɪɹɞɭ ɫ ɹɞɟɪɧɵɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɦɟɠɞɭ ɧɭɤɥɨɧɚɦɢ, ɭɱɢɬɵɜɚɸɬɫɹ ɬɚɤɠɟ ɢ ɤɭɥɨɧɨɜɫɤɨɟ ɜɡɚɢɦɨɨɬɬɚɥɤɢɜɚɧɢɟ ɩɪɨɬɨɧɨɜ, ɢ ɫɜɹɡɚɧɧɚɹ ɫ ɷɬɢɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɧɟɫɮɟɪɢɱɧɨɫɬɶ ɹɞɟɪ. ɉɨɫɥɟɞɧɟɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɩɪɢɜɨɞɢɬ ɤ ɬɨɦɭ, ɱɬɨ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɬɹɠɟɥɵɯ ɹɞɟɪ ɫɤɥɚɞɵɜɚɸɬɫɹ ɧɟ ɬɨɥɶɤɨ ɢɡ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ «ɜɧɟɲɧɢɯ» ɧɭɤɥɨɧɨɜ, ɧɨ ɬɚɤɠɟ ɢɡ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ, ɫɜɹɡɚɧɧɨɝɨ ɫ ɜɪɚɳɟɧɢɟɦ ɚɤɫɢɚɥɶɧɨ-ɫɢɦɦɟɬɪɢɱɧɨɝɨ ɹɞɪɚ.
ɂɬɚɤ, ɹɞɪɨ, ɨɛɥɚɞɚɸɳɟɟ ɫɩɢɧɨɦ, ɢɦɟɟɬ ɦɨɦɟɧɬ ɤɨɥɢɱɟɫɬɜɚ ɞɜɢɠɟɧɢɹ, ɪɚɜɧɵɣ ɩɨ ɦɨɞɭɥɸ
G I (I 1)=, (5.1)
ɝɞɟ I = 0; 1/2; 1; 3/2; 2; … . Ɇɚɝɧɢɬɧɨɟ ɤɜɚɧɬɨɜɨɟ ɱɢɫɥɨ ml ɩɪɢ ɡɚɞɚɧɧɨɦ I ɩɪɢɧɢɦɚɟɬ (2l + 1) ɡɧɚɱɟɧɢɣ:
ml = I, I – 1, …, 0, ..., –(I – 1), – I.
Ɇɟɯɚɧɢɱɟɫɤɨɦɭ ɦɨɦɟɧɬɭ G ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ |
|
ȝI = gɹɞ I (I 1) ȝɹɞ, |
(5.2) |
ɝɞɟ gɹɞ – ɹɞɟɪɧɨɟ ɝɢɪɨɦɚɝɧɢɬɧɨɟ ɨɬɧɨɲɟɧɢɟ. |
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5.2. ɗɥɟɤɬɪɨɧɧɵɣ ɢ ɹɞɟɪɧɵɣ ɦɚɝɧɢɬɧɵɟ ɪɟɡɨɧɚɧɫɵ
ɉɪɢ ɜɧɟɫɟɧɢɢ ɤɪɢɫɬɚɥɥɚ, ɫɨɞɟɪɠɚɳɟɝɨ ɩɚɪɚɦɚɝɧɢɬɧɵɟ ɢɨɧɵ ɢɥɢ ɚɬɨɦɵ, ɜ ɩɨɫɬɨɹɧɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɩɨɞ ɩɪɹɦɵɦ ɭɝɥɨɦ ɤ ɤɨɬɨɪɨɦɭ ɩɨɞɚɟɬɫɹ ɩɟɪɟɦɟɧɧɨɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɫ ɱɚɫɬɨɬɨɣ Ȧ, ɧɚɛɥɸɞɚɸɬɫɹ ɞɢɫɩɟɪɫɢɹ ɦɚɝɧɢɬɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɢ ɩɨɝɥɨɳɟɧɢɟ ɷɧɟɪɝɢɢ ɩɟɪɟɦɟɧɧɨɝɨ ɩɨɥɹ. ɉɨɝɥɨɳɟɧɢɟ ɧɨɫɢɬ ɹɪɤɨ ɜɵɪɚɠɟɧɧɵɣ ɪɟɡɨɧɚɧɫɧɵɣ ɯɚɪɚɤɬɟɪ.
Ɋɟɡɨɧɚɧɫɧɵɟ ɹɜɥɟɧɢɹ ɨɛɭɫɥɨɜɥɟɧɵ ɷɮɮɟɤɬɨɦ Ɂɟɟɦɚɧɚ, ɬ. ɟ. ɪɚɫɳɟɩɥɟɧɢɟɦ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɪɨɜɧɟɣ ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɫɢɥɶɧɨɝɨ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɪɢ ɪɟɡɨɧɚɧɫɟ ɜɨɡɧɢɤɚɟɬ ɩɨɝɥɨɳɟɧɢɟ ɷɧɟɪɝɢɢ ɩɟɪɟɦɟɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɫɬɪɨɝɨ ɨɩɪɟɞɟɥɟɧɧɵɯ ɱɚɫɬɨɬɚɯ, ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɪɚɡɪɟɲɟɧɧɵɦ ɦɟɠɭɪɨɜɧɟɜɵɦ ɩɟɪɟɯɨɞɚɦ. Ʉɚɤ ɩɪɚɜɢɥɨ, ɪɟɡɨɧɚɧɫ ɧɚɛɥɸɞɚɸɬ, ɤɨɝɞɚ ɩɪɢɥɨɠɟɧɨ ɩɨɩɟɪɟɱɧɨɟ ɩɟɪɟɦɟɧɧɨɟ ɩɨɥɟ ȼɑɢɥɢ ɋȼɑ-ɞɢɚɩɚɡɨɧɚ ɥɚɪɦɨɪɨɜɫɤɨɣ ɱɚɫɬɨɬɵ.
ɉɨɫɬɨɹɧɧɨɟ ɨɞɧɨɪɨɞɧɨɟ ɩɨɥɟ, ɩɪɢɥɨɠɟɧɧɨɟ ɜ ɧɚɩɪɚɜɥɟɧɢɢ z, ɜɵɡɵɜɚɟɬ ɩɪɟɰɟɫɫɢɸ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɫ ɥɚɪɦɨɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ Ȧ0. ȼɑ-ɩɨɥɟ bx 2b1 cos Zt ɩɪɢɥɨɠɟɧɨ ɜ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɩɥɨɫɤɨ-
ɫɬɢ. ɍɞɨɛɧɨ ɩɨɥɚɝɚɬɶ, ɱɬɨ bx ɹɜɥɹɟɬɫɹ ɫɭɦɦɨɣ ɞɜɭɯ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɜɪɚɳɚɸɳɢɯɫɹ ɩɨɥɟɣ 2b1 cosZt b1 eiZt e iZt (ɪɢɫ. 5.2). Ɋɟɡɨɧɚɧɫ
ɢɦɟɟɬ ɦɟɫɬɨ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɩɪɟɰɟɫɫɢɹ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɩɪɨɢɫɯɨɞɢɬ ɫɢɧɯɪɨɧɧɨ ɫ ɨɞɧɨɣ ɢɡ ɤɨɦɩɨɧɟɧɬ ɩɟɪɟɦɟɧɧɨɝɨ ɩɨɥɹ. Ɋɟɡɨɧɚɧɫ ɧɟ ɜɨɡɧɢɤɚɟɬ, ɟɫɥɢ b1 ɩɚɪɚɥɥɟɥɶɧɨ B0.
ɍɩɪɨɳɟɧɧɚɹ ɫɯɟɦɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 5.3.
Ɋɢɫ. 5.2. ɉɟɪɟɦɟɧɧɨɟ ɩɨɥɟ |
Ɋɢɫ. 5.3. ɋɯɟɦɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ |
ɪɚɡɥɨɠɟɧɨ ɧɚ ɞɜɟ ɫɨɫɬɚɜɥɹɸɳɢɟ |
ɭɫɬɚɧɨɜɤɢ |
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