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Ɏ ɁȻɚɞɚɟɜ
ɏɂɆɂə ɆȿɌȺɅɅɈȼ
ɍɱɟɛɧɨɟɩɨɫɨɛɢɟ
Ɇɨɫɤɜɚ ȼɨɥɨɝɞɚ
©ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹª
2024
ɍȾɄ 546
ȻȻɄ 24.1
Ȼ
Ɋɟɰɟɧɡɟɧɬɵ
ɤɚɧɞɢɞɚɬɯɢɦɢɱɟɫɤɢɯɧɚɭɤɞɨɰɟɧɬɋɦɢɪɧɨɜȺ Ⱦ ɆȽɌɍɢɦɇ ɗȻɚɭɦɚɧɚ);
ɤɚɧɞɢɞɚɬɯɢɦɢɱɟɫɤɢɯɧɚɭɤɞɨɰɟɧɬɍɱɟɜɚɬɤɢɧɚɇ ȼ
Ɇɨɫɤɨɜɫɤɢɣɦɟɠɞɭɧɚɪɨɞɧɵɣɭɧɢɜɟɪɫɢɬɟɬ
ȻɚɞɚɟɜɎɁ
Ȼ ɏɢɦɢɹɦɟɬɚɥɥɨɜɭɱɟɛɧɨɟɩɨɫɨɛɢɟɎɁȻɚɞɚɟɜ– Ɇɨɫɤɜɚȼɨɥɨɝɞɚ
ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹ– 128 ɫɢɥɬɚɛɥ
ISBN 978-5-9729-1857-7
Ʉɪɚɬɤɨ ɢɡɥɨɠɟɧɵ ɨɛɳɢɟ ɫɜɨɣɫɬɜɚ ɦɟɬɚɥɥɨɜ ɦɟɬɨɞɵ ɢɯ ɩɨɥɭɱɟɧɢɹ
ɨɫɨɛɟɧɧɨɫɬɢɢɯɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨɫɬɪɨɟɧɢɹɞɚɧɚɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯɢɦɢɱɟ
ɫɤɢɯ ɫɜɨɣɫɬɜ s-p- d-ɷɥɟɦɟɧɬɨɜ ɉɪɢɷɬɨɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ d-ɷɥɟɦɟɧɬɨɜ
ɪɚɫɫɦɨɬɪɟɧɚɜɫɨɨɬɜɟɬɫɬɜɢɢɫɢɯɩɨɥɨɠɟɧɢɟɦɜɩɟɪɢɨɞɚɯɉɨɞɪɨɛɧɨɪɚɫ
ɫɦɨɬɪɟɧɵɯɢɦɢɱɟɫɤɢɟɫɜɨɣɫɬɜɚd-ɷɥɟɦɟɧɬɨɜɱɟɬɜɺɪɬɨɝɨɩɟɪɢɨɞɚɤɨɬɨɪɵɟ
ɧɚɢɛɨɥɟɟ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬɞɥɹ ɫɨɡɞɚɧɢɹ ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɯ ɦɚɬɟɪɢɚɥɨɜ
ɉɪɢɜɟɞɟɧɵɩɪɢɦɟɪɵɪɟɲɟɧɢɹɡɚɞɚɱɢɤɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ
Ⱦɥɹɫɬɭɞɟɧɬɨɜɢɧɠɟɧɟɪɧɵɯɫɩɟɰɢɚɥɶɧɨɫɬɟɣɢɡɭɱɚɸɳɢɯɞɢɫɰɢɩɥɢɧɵ
©ɏɢɦɢɹªɢ©ɇɟɨɪɝɚɧɢɱɟɫɤɚɹɯɢɦɢɹª
ɍȾɄ
ȻȻɄ
ISBN 978-5-9729-1857-7 ȻɚɞɚɟɜɎɁ
ɂɡɞɚɬɟɥɶɫɬɜɨ©ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹª
Ɉɮɨɪɦɥɟɧɢɟɂɡɞɚɬɟɥɶɫɬɜɨ©ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹª
2
ɈȽɅȺȼɅȿɇɂȿ
ȼɜɟɞɟɧɢɟ ....................................................................................................................... 4
Ɉɛɳɢɟɫɜɨɣɫɬɜɚɢɩɨɥɭɱɟɧɢɟɦɟɬɚɥɥɨɜ ............................................................ 5
ɗɥɟɤɬɪɨɧɧɨɟɫɬɪɨɟɧɢɟɷɥɟɦɟɧɬɨɜ-ɦɟɬɚɥɥɨɜ ............................................. 5
Ɉɫɧɨɜɧɵɟɮɢɡɢɱɟɫɤɢɟɫɜɨɣɫɬɜɚɦɟɬɚɥɥɨɜ ................................................. 6
Ʉɪɢɫɬɚɥɥɢɱɟɫɤɢɟɫɬɪɭɤɬɭɪɵɦɟɬɚɥɥɨɜ ...................................................... 8
Ɉɫɧɨɜɧɵɟɫɩɨɫɨɛɵɩɨɥɭɱɟɧɢɹɦɟɬɚɥɥɨɜ ................................................. 17
ɏɢɦɢɱɟɫɤɢɟɫɜɨɣɫɬɜɚɦɟɬɚɥɥɨɜ ................................................................ 20
ɉɪɢɦɟɪɵɪɟɲɟɧɢɹɡɚɞɚɱ ................................................................................... 27
Ʉɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ ...................................................................................... 29
s-ɗɥɟɦɟɧɬɵ-ɦɟɬɚɥɥɵ .......................................................................................... 30
ɗɥɟɦɟɧɬɵɩɟɪɜɨɣɝɪɭɩɩɵ ......................................................................... 30
ɗɥɟɦɟɧɬɵɜɬɨɪɨɣɝɪɭɩɩɵ ......................................................................... 38
ɉɪɢɦɟɪɵɪɟɲɟɧɢɹɡɚɞɚɱ ................................................................................... 46
Ʉɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ ...................................................................................... 47
ɪ-ɗɥɟɦɟɧɬɵ-ɦɟɬɚɥɥɵ .......................................................................................... 50
Ɉɛɳɚɹɯɚɪɚɤɬɟɪɢɫɬɢɤɚɮɢɡɢɱɟɫɤɢɯ
ɢɯɢɦɢɱɟɫɤɢɯɫɜɨɣɫɬɜp-ɷɥɟɦɟɧɬɨɜ-ɦɟɬɚɥɥɨɜ ................................................ 51
Ⱥɥɸɦɢɧɢɣ ................................................................................................... 55
Ɉɥɨɜɨ ........................................................................................................... 59
ɋɜɢɧɟɰ ......................................................................................................... 64
ɉɪɢɦɟɪɵɪɟɲɟɧɢɹɡɚɞɚɱ ................................................................................... 69
Ʉɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ ...................................................................................... 71
d-ɗɥɟɦɟɧɬɵ ........................................................................................................... 74
Ɉɛɳɚɹɯɚɪɚɤɬɟɪɢɫɬɢɤɚɮɢɡɢɱɟɫɤɢɯ
ɢɯɢɦɢɱɟɫɤɢɯɫɜɨɣɫɬɜd-ɷɥɟɦɟɧɬɨɜ ................................................................. 74
Ɉɛɳɚɹɯɚɪɚɤɬɟɪɢɫɬɢɤɚ d-ɷɥɟɦɟɧɬɨɜɱɟɬɜɟɪɬɨɝɨɩɟɪɢɨɞɚ ...................... 79
ɏɪɨɦ ............................................................................................................. 84
ɀɟɥɟɡɨ ......................................................................................................... 93
ɇɢɤɟɥɶ ....................................................................................................... 105
4.6Ɇɟɞɶ ........................................................................................................... 111
ɉɪɢɦɟɪɵɪɟɲɟɧɢɹɡɚɞɚɱ ......................................................................................... 119
Ʉɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ ............................................................................................. 121
Ɂɚɤɥɸɱɟɧɢɟ ............................................................................................................... 123
ɋɩɢɫɨɤɥɢɬɟɪɚɬɭɪɵ.................................................................................................. 124
3
ȼȼȿȾȿɇɂȿ
Ɉɛɳɟɩɪɢɧɹɬɨɞɟɥɟɧɢɟɷɥɟɦɟɧɬɨɜɧɚɦɟɬɚɥɥɵ ɢɧɟɦɟɬɚɥɥɵ. ɂɡɨɬɤɪɵ
ɬɵɯ ɤ ɧɚɫɬɨɹɳɟɦɭ ɜɪɟɦɟɧɢ ɷɥɟɦɟɧɬɨɜ ɤ ɧɟɦɟɬɚɥɥɚɦ ɨɬɧɨɫɹɬ 6 ɷɥɟɦɟɧɬɨɜ.
Ʉɦɟɬɚɥɥɚɦ ɨɬɧɨɫɹɬ ɜɫɟɨɫɬɚɥɶɧɵɟɷɥɟɦɟɧɬɵ ɂɧɨɝɞɚɞɥɹɷɥɟɦɟɧɬɨɜɩɪɨɹɜɥɹ
ɸɳɢɯɫɥɚɛɨɜɵɪɚɠɟɧɧɵɟɦɟɬɚɥɥɢɱɟɫɤɢɟɫɜɨɣɫɬɜɚɢɫɩɨɥɶɡɭɸɬɬɟɪɦɢɧɩɨɥɭɦɟ
ɬɚɥɥ ɢɥɢɦɟɬɚɥɥɨɢɞ.
Ɇɟɬɚɥɥɵɢɢɯɫɨɟɞɢɧɟɧɢɹɢɝɪɚɸɬɜɚɠɧɭɸɪɨɥɶɜɦɢɧɟɪɚɥɶɧɨɣɢɨɪɝɚɧɢɱɟ
ɫɤɨɣɠɢɡɧɢɁɟɦɥɢȺɬɨɦɵɢɢɨɧɵɦɟɬɚɥɥɨɜɜɯɨɞɹɬɜɫɨɫɬɚɜɜɚɠɧɟɣɲɢɯɫɨɟɞɢ
ɧɟɧɢɣɭɱɚɫɬɜɭɸɳɢɯɜɠɢɡɧɟɞɟɹɬɟɥɶɧɨɫɬɢɪɚɫɬɟɧɢɣɠɢɜɨɬɧɵɯɢɱɟɥɨɜɟɤɚ
Ɇɟɬɚɥɥɵɢ ɢɯ ɫɩɥɚɜɵ ɫɥɭɠɚɬ ɨɫɧɨɜɧɵɦ ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɦɦɚɬɟɪɢɚɥɨɦ ɜ
ɦɚɲɢɧɨɫɬɪɨɟɧɢɢɢ ɩɪɢɛɨɪɨɫɬɪɨɟɧɢɢɂɧɠɟɧɟɪɚ-ɦɟɯɚɧɢɤɚɢɩɪɢɛɨɪɨɫɬɪɨɢɬɟɥɹ
ɨɫɨɛɟɧɧɨɢɧɬɟɪɟɫɭɸɬɯɚɪɚɤɬɟɪɢɫɬɢɤɢɦeɬɚɥɥɚɤɚɤɤɨɧɫɬɪɭɤɰɢɨɧɧɨɝɨɦɚɬɟɪɢɚ
ɥɚɬɨɟɫɬɶɜɬɜɟɪɞɨɦɤɨɦɩɚɤɬɧɨɦɫɨɫɬɨɹɧɢɢɫɨɩɪɟɞɟɥɟɧɧɵɦɤɨɦɩɥɟɤɫɨɦɮɢ
ɡɢɱɟɫɤɢɯɫɜɨɣɫɬɜɉɪɢɦɟɧɟɧɢɟɦɟɬɚɥɥɨɜɧɟɜɨɡɦɨɠɧɨ ɢ ɛɟɡɡɧɚɧɢɹɢɯ ɯɢɦɢɱɟ
ɫɤɢɯɫɜɨɣɫɬɜɬɚɤɤɚɤɷɬɢɦɨɩɪɟɞɟɥɹɟɬɫɹɢɯɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɶɜɭɫɥɨɜɢɹɯɷɤɫ
ɩɥɭɚɬɚɰɢɢ ɉɨɷɬɨɦɭ ɜ ɞɚɧɧɨɦ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɯɢɦɢɱɟɫɤɢɟ ɢ ɮɢɡɢɱɟɫɤɢɟ
ɫɜɨɣɫɬɜɚɦɟɬɚɥɥɨɜɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹɜɧɟɪɚɡɪɵɜɧɨɣɫɜɹɡɢ
4
ɈȻɓɂȿɋȼɈɃɋɌȼȺɂɉɈɅɍɑȿɇɂȿɆȿɌȺɅɅɈȼ
ɉɪɨɫɬɵɟɜɟɳɟɫɬɜɚɨɛɪɚɡɨɜɚɧɧɵɟɷɥɟɦɟɧɬɚɦɢɝɪɭɩɩɢs-ɷɥɟɦɟɧɬɚɦɢɚ
ɬɚɤɠɟd-ɷɥɟɦɟɧɬɚɦɢ ɹɜɥɹɸɬɫɹɦɟɬɚɥɥɚɦɢ ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢp-ɷɥɟɦɟɧɬɨɜɦɟ
ɬɚɥɥɵ ɦɨɠɧɨ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɨɬɞɟɥɢɬɶ ɨɬ ɧɟɦɟɬɚɥɥɨɜ ɞɢɚɝɨɧɚɥɶɧɨɣ ɥɢɧɢɟɣ
ɪɢɫ
ɗɥɟɤɬɪɨɧɧɨɟɫɬɪɨɟɧɢɟɷɥɟɦɟɧɬɨɜ-ɦɟɬɚɥɥɨɜ
ɉɨ ɫɜɨɟɦɭ ɷɥɟɤɬɪɨɧɧɨɦɭ ɫɬɪɨɟɧɢɸ ɦɟɬɚɥɥɵ ɞɟɥɹɬɫɹ ɧɚ s- p- d- ɢ
f-ɦɟɬɚɥɥɵ s-ɦɟɬɚɥɥɵ ɪɚɫɩɨɥɨɠɟɧɵ ɜ ɢ ɝɪɭɩɩɚɯ ɉɟɪɢɨɞɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
ɯɢɦɢɱɟɫɤɢɯɷɥɟɦɟɧɬɨɜɪ-ɦɟɬɚɥɥɵ– ɜɝɪɭɩɩɚɯȼɫɟɨɧɢɡɚɢɫɤɥɸɱɟ
ɧɢɟɦ ɨɥɨɜɚ ɫɜɢɧɰɚ ɜɢɫɦɭɬɚ ɧɚ ɜɧɟɲɧɟɦ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɭɪɨɜɧɟ ɢɦɟɸɬ
1–ɷɥɟɤɬɪɨɧɚ
ɇɨɦɟɪɝɪɭɩɩɵ
13 14 15 16 17 18
B C N O F Ne
Al Si P S Cl Ar
Ga Ge As Se Br Kr
In Sn Sb Te I Xe
Tl Pb Bi Po At Rn
Ɋɢɫ©Ⱦɢɚɝɨɧɚɥɶɧɚɹɥɢɧɢɹªɩɪɢɛɥɢɡɢɬɟɥɶɧɨɪɚɡɞɟɥɹɸɳɚɹɩɨɥɨɠɟɧɢɹ
ɧɟɦɟɬɚɥɥɨɜɫɩɪɚɜɚɨɬɬɨɥɫɬɨɣɥɢɧɢɢɢɦɟɬɚɥɥɨɜɫɥɟɜɚɨɬɬɨɥɫɬɨɣɥɢɧɢɢ
ɗɥɟɤɬɪɨɧɧɵɟ ɤɨɧɮɢɝɭɪɚɰɢɢ ɜɧɟɲɧɟɝɨ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɭɪɨɜɧɹ s- ɢ
ɪ-ɷɥɟɦɟɧɬɨɜ-ɦɟɬɚɥɥɨɜɩɪɢɜɟɞɟɧɵɜɬɚɛɥ ȼɝɪɭɩɩɚɯs- ɢɪ-ɷɥɟɦɟɧɬɨɜɱɢɫɥɨ
ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɜɧɟɲɧɟɦ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɭɪɨɜɧɟ ɧɟ ɢɡɦɟɧɹɟɬɫɹ ɪɚɞɢɭɫ ɚɬɨɦɚ
ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫɜɟɪɯɭ ɜɧɢɡ ɩɨ ɝɪɭɩɩɟ ɷɥɟɤɬɪɨɨɬɪɢɰɚɬɟɥɶɧɨɫɬɶ ɭɦɟɧɶɲɚɟɬɫɹ
ɫɜɟɪɯɭɜɧɢɡɩɨ ɝɪɭɩɩɟ ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɟɚɫɥɟɞɨɜɚɬɟɥɶɧɨɢ ɦɟɬɚɥɥɢɱɟɫɤɢɟ
ɫɜɨɣɫɬɜɚɭɫɢɥɢɜɚɸɬɫɹ
ɇɚɱɢɧɚɹɫɩɟɪɢɨɞɚɩɨɹɜɥɹɸɬɫɹɜɫɬɚɜɧɵɟɞɟɤɚɞɵd-ɷɥɟɦɟɧɬɨɜɭɤɨɬɨɪɵɯ
ɡɚɩɨɥɧɹɟɬɫɹɩɪɟɞɜɧɟɲɧɢɣɷɧɟɪɝɟɬɢɱɟɫɤɢɣd-ɩɨɞɭɪɨɜɟɧɶd-ɗɥɟɦɟɧɬɵ ɪɚɫɩɨɥɨ
ɠɟɧɵɜ –12 ɝɪɭɩɩɚɯɉɟɪɢɨɞɢɱɟɫɤɨɣɫɢɫɬɟɦɵ ɯɢɦɢɱɟɫɤɢɯɷɥɟɦɟɧɬɨɜɜɫɟ ɨɧɢ
ɹɜɥɹɸɬɫɹ ɦɟɬɚɥɥɚɦɢ ɢɦɟɸɬ ɛɨɥɶɲɨɟ ɤɨɥɢɱɟɫɬɜɨ ɜɚɥɟɧɬɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɬɚɤ
ɤɚɤɢɦɢ ɹɜɥɹɸɬɫɹ ɧɟ ɬɨɥɶɤɨ s-ɧɨ ɢ d-ɷɥɟɤɬɪɨɧɵɗɬɨ ɫɜɨɣɫɬɜɨɨɛɟɫɩɟɱɢɜɚɟɬ
5
ɛɨɥɶɲɨɟ ɪɚɡɧɨɨɛɪɚɡɢɟɫɬɟɩɟɧɟɣ ɨɤɢɫɥɟɧɢɹ ɢ ɹɪɤɨ ɜɵɪɚɠɟɧɧɭɸ ɫɤɥɨɧɧɨɫɬɶ ɤ
ɤɨɦɩɥɟɤɫɨɨɛɪɚɡɨɜɚɧɢɸ
Ɍɚɛɥɢɰɚ
ɗɥɟɤɬɪɨɧɧɵɟɤɨɧɮɢɝɭɪɚɰɢɢɜɧɟɲɧɟɝɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨɭɪɨɜɧɹ ɚɬɨɦɨɜ
s- ɢɪ-ɷɥɟɦɟɧɬɨɜ-ɦɟɬɚɥɥɨɜ
ns
1
ns
2
ns2 np
1
ns2 np
2
ns2 np
3
Li Be
Na Mg Al
K Ca Ga
Rb Sr In Sn
Cs Ba Tl Pb Bi
ɇɚɩɪɢɦɟɪd-ɷɥɟɦɟɧɬɚɦ-ɝɨɩɟɪɢɨɞɚɨɬɜɟɱɚɸɬɷɥɟɤɬɪɨɧɧɵɟɤɨɧɮɢɝɭɪɚɰɢɢ
n4s2
[Ar]3d
ɂɫɤɥɸɱɟɧɢɟɫɨɫɬɚɜɥɹɸɬCr ([Ar]3d54s1ɢCu ([Ar]3d104s1ɞɥɹɤɨɬɨ
ɪɵɯɧɚɛɥɸɞɚɟɬɫɹ©ɩɪɨɜɚɥªɷɥɟɤɬɪɨɧɚɱɬɨɨɛɴɹɫɧɹɟɬɫɹɩɨɜɵɲɟɧɧɨɣɭɫɬɨɣɱɢɜɨ
ɫɬɶɸɧɚɩɨɥɨɜɢɧɭɡɚɩɨɥɧɟɧɧɨɝɨɢɩɨɥɧɨɫɬɶɸɡɚɩɨɥɧɟɧɧɨɝɨ d-ɩɨɞɭɪɨɜɧɹ
ȼ ɝɪɭɩɩɚɯ d-ɷɥɟɦɟɧɬɨɜ ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɜɧɟɲɧɟɦ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦ
ɭɪɨɜɧɟ ɧɟ ɢɡɦɟɧɹɟɬɫɹ ɪɚɞɢɭɫ ɚɬɨɦɚ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɯɨɬɹ ɜ ɦɟɧɶɲɟɣ ɫɬɟɩɟɧɢ
ɱɟɦ ɭ s- ɢ ɪ-ɷɥɟɦɟɧɬɨɜ-ɦɟɬɚɥɥɨɜ ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɱɚɳɟ ɜɫɟɝɨ
ɭɦɟɧɶɲɚɸɬɫɹɭɫɬɨɣɱɢɜɨɫɬɶɜɵɫɲɟɣɫɬɟɩɟɧɢɨɤɢɫɥɟɧɢɹɭɜɟɥɢɱɢɜɚɟɬɫɹ
ɇɚɱɢɧɚɹ ɫ ɩɟɪɢɨɞɚ ɩɨɹɜɥɹɸɬɫɹ ɫɟɦɟɣɫɬɜɚ ɥɚɧɬɚɧɨɢɞɨɜ ɢ ɚɤɬɢɧɨɢɞɨɜ
ɤɨɬɨɪɵɟɜɤɥɸɱɚɸɬɩɨf-ɷɥɟɦɟɧɬɨɜɭɧɢɯɡɚɩɨɥɧɹɟɬɫɹɬɪɟɬɢɣɫɤɨɧɰɚɷɧɟɪɝɟ
ɬɢɱɟɫɤɢɣɭɪɨɜɟɧɶf-ɗɥɟɦɟɧɬɵɪɚɫɩɨɥɨɠɟɧɵɜɝɪɭɩɩɟɉɟɪɢɨɞɢɱɟɫɤɨɣɫɢɫɬɟ
ɦɵɯɢɦɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ ɢɯɷɥɟɤɬɪɨɧɧɚɹɤɨɧɮɢɝɭɪɚɰɢɹɢɦɟɟɬ ɜɢɞn-2)f
0-1 ns2
(n-1)d
ȼɫɟɨɧɢɹɜɥɹɸɬɫɹɦɟɬɚɥɥɚɦɢɩɪɨɹɜɥɹɸɬɨɱɟɧɶɫɯɨɠɢɟɯɢɦɢɱɟɫɤɢɟ
1-14
ɫɜɨɣɫɬɜɚ
Ɉɫɧɨɜɧɵɟɮɢɡɢɱɟɫɤɢɟɫɜɨɣɫɬɜɚɦɟɬɚɥɥɨɜ
Ɇɟɬɚɥɥɵ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɪɹɞɨɦ ɫɯɨɞɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɤɨɬɨɪɵɟ
ɨɬɥɢɱɚɸɬɢɯɨɬɧɟɦɟɬɚɥɥɨɜ
6
1. Ɇɟɬɚɥɥɢɱɟɫɤɢɣɛɥɟɫɤ ɫɩɨɫɨɛɧɨɫɬɶɩɨɜɟɪɯɧɨɫɬɢɦɟɬɚɥɥɚɨɬɪɚɠɚɬɶɫɜɟ
ɬɨɜɵɟɥɭɱɢɗɬɨɫɜɹɡɚɧɨɫɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦɫɜɨɛɨɞɧɵɯɷɥɟɤɬɪɨɧɨɜɫɩɚɞɚɸɳɢ
ɦɢɧɚɦɟɬɚɥɥɤɜɚɧɬɚɦɢɫɜɟɬɚ
2. ɉɥɚɫɬɢɱɧɨɫɬɶ ɫɩɨɫɨɛɧɨɫɬɶɢɡɦɟɧɹɬɶɮɨɪɦɭɩɪɢɭɞɚɪɟɜɵɬɹɝɢɜɚɬɶɫɹɜ
ɩɪɨɜɨɥɨɤɭɩɪɨɤɚɬɵɜɚɬɶɫɹɜ ɬɨɧɤɢɟɥɢɫɬɵ ɇɚɩɪɢɦɟɪɜ ɪɹɞɭ$X $J&X 6Q
=Q)Hɩɥɚɫɬɢɱɧɨɫɬɶɭɦɟɧɶɲɚɟɬɫɹɋɚɦɵɦɩɥɚɫɬɢɱɧɵɦɢ ɤɨɜɤɢɦɦɟɬɚɥɥɨɦɹɜ
ɥɹɟɬɫɹɡɨɥɨɬɨɢɡɧɟɝɨɦɨɠɧɨɢɡɝɨɬɨɜɢɬɶɬɨɧɱɚɣɲɭɸɩɪɨɜɨɥɨɤɭɢɥɢɩɪɨɤɚɬɚɬɶ
ɟɝɨɜɥɢɫɬɵɬɨɥɳɢɧɨɣ–3 – 10–4 ɦɦ
3. ɗɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɷɬɨɫɜɨɣɫɬɜɨɜɟɳɟɫɬɜɚɩɪɨɜɨɞɢɬɶɷɥɟɤɬɪɢɱɟɫɤɢɣ
ɬɨɤɈɛɴɹɫɧɹɟɬɫɹɧɚɩɪɚɜɥɟɧɧɵɦɞɜɢɠɟɧɢɟɦ ɫɜɨɛɨɞɧɵɯ ɷɥɟɤɬɪɨɧɨɜɨɬɨɬɪɢɰɚ
ɬɟɥɶɧɨɝɨɩɨɥɸɫɚ ɤ ɩɨɥɨɠɢɬɟɥɶɧɨɦɭɩɨɞ ɜɥɢɹɧɢɟɦɧɟɛɨɥɶɲɨɣɪɚɡɧɨɫɬɢɩɨɬɟɧ
ɰɢɚɥɨɜȼɷɥɟɤɬɪɢɱɟɫɤɨɦɩɨɥɟɦɢɝɪɢɪɭɸɳɢɟɢɥɢɨɛɨɛɳɟɧɧɵɟɷɥɟɤɬɪɨɧɵɩɨɥɭ
ɱɚɸɬɧɚɩɪɚɜɥɟɧɧɨɟɞɜɢɠɟɧɢɟ– ɷɥɟɤɬɪɢɱɟɫɤɢɣɬɨɤɌɚɤɨɟɫɨɫɬɨɹɧɢɟɷɥɟɤɬɪɨɧɨɜ
ɧɚɡɵɜɚɟɬɫɹɫɨɫɬɨɹɧɢɟɦɩɪɨɜɨɞɢɦɨɫɬɢ
ȼɪɹɞɭ $J&X $O)H ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶɭɦɟɧɶɲɚɟɬɫɹɉɪɢ ɧɚɝɪɟɜɚɧɢɢ
ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɦɟɬɚɥɥɨɜ ɭɦɟɧɶɲɚɟɬɫɹ ɬ ɤɫɩɨɜɵɲɟɧɢɟɦɬɟɦɩɟɪɚɬɭɪɵ
ɭɫɢɥɢɜɚɸɬɫɹɤɨɥɟɛɚɧɢɹɚɬɨɦɨɜɢɢɨɧɨɜɜɭɡɥɚɯɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣɪɟɲɟɬɤɢɱɬɨ
ɭɦɟɧɶɲɚɟɬɩɨɞɜɢɠɧɨɫɬɶɷɥɟɤɬɪɨɧɨɜ
4. Ɍɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶ ɷɬɨ ɫɩɨɫɨɛɧɨɫɬɶɬɟɥɚɩɟɪɟɞɚɜɚɬɶ ɬɟɩɥɨɬɭ ɨɬɛɨɥɟɟ
ɧɚɝɪɟɬɵɯɟɝɨɱɚɫɬɟɣɦɟɧɟɟɧɚɝɪɟɬɵɦɈɧɚɨɛɭɫɥɨɜɥɟɧɚɜɵɫɨɤɨɣɩɨɞɜɢɠɧɨɫɬɶɸ
ɫɜɨɛɨɞɧɵɯɷɥɟɤɬɪɨɧɨɜɢɤɨɥɟɛɚɬɟɥɶɧɵɦɞɜɢɠɟɧɢɟɦɚɬɨɦɨɜɛɥɚɝɨɞɚɪɹ ɱɟɦɭ
ɩɪɨɢɫɯɨɞɢɬɛɵɫɬɪɨɟɜɵɪɚɜɧɢɜɚɧɢɟɬɟɦɩɟɪɚɬɭɪɵɩɨɦɚɫɫɟɦɟɬɚɥɥɚɇɚɢɛɨɥɶɲɟɣ
ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶɸɨɛɥɚɞɚɸɬɜɢɫɦɭɬɢɪɬɭɬɶ
5. Ɍɜɟɪɞɨɫɬɶ ɷɬɨ ɫɩɨɫɨɛɧɨɫɬɶ ɫɜɨɣɫɬɜɨɬɜɟɪɞɨɝɨ ɬɟɥɚɫɨɩɪɨɬɢɜɥɹɬɶɫɹ
ɩɪɨɧɢɤɧɨɜɟɧɢɸɜɧɟɝɨɞɪɭɝɨɝɨɬɟɥɚɇɚɩɪɢɦɟɪɫɚɦɵɦ ɬɜɟɪɞɵɦ ɦɟɬɚɥɥɨɦɹɜɥɹ
ɟɬɫɹ ɯɪɨɦ ɪɟɠɟɬ ɫɬɟɤɥɨ ɫɚɦɵɦɢ ɦɹɝɤɢɦɢ – ɳɟɥɨɱɧɵɟ ɦɟɬɚɥɥɵ ɤɚɥɢɣ
ɧɚɬɪɢɣɪɭɛɢɞɢɣɢɰɟɡɢɣɪɟɠɭɬɫɹɧɨɠɨɦ
6. ɉɥɨɬɧɨɫɬɶ ȡ ɷɬɨɮɢɡɢɱɟɫɤɚɹɜɟɥɢɱɢɧɚɢɡɦɟɪɹɟɦɚɹɨɬɧɨɲɟɧɢɟɦ
ɦɚɫɫɵɬɟɥɚɤɟɝɨɨɛɴɟɦɭɈɧɚɬɟɦɦɟɧɶɲɟɱɟɦɦɟɧɶɲɟɚɬɨɦɧɚɹɦɚɫɫɚɦɟɬɚɥɥɚɢ
ɱɟɦɛɨɥɶɲɟ ɪɚɞɢɭɫɟɝɨ ɚɬɨɦɚɋɚɦɵɣ ɥɟɝɤɢɣɦɟɬɚɥɥ ɥɢɬɢɣ U ɝɫɦ3);
ɫɚɦɵɣ ɬɹɠɟɥɵɣ – ɨɫɦɢɣ U ɝɫɦ3 Ɇɟɬɚɥɥɵ ɢɦɟɸɳɢɟ ɩɥɨɬɧɨɫɬɶ
U ɝɫɦ3 ɧɚɡɵɜɚɸɬ ©ɥɟɝɤɢɦɢɦɟɬɚɥɥɚɦɢª ɧɚɩɪɢɦɟɪ Li Ca Na Mg Alɚ
ɦɟɬɚɥɥɵ ɢɦɟɸɳɢɟ ɩɥɨɬɧɨɫɬɶ U ! ɝɫɦ3 ɧɚɡɵɜɚɸɬ ©ɬɹɠɺɥɵɦɢ ɦɟɬɚɥɥɚɦɢª
ɧɚɩɪɢɦɟɪ$JPbTa).
7. Ɍɟɦɩɟɪɚɬɭɪɚɩɥɚɜɥɟɧɢɹ (T
)
ɷɬɨ ɬɟɦɩɟɪɚɬɭɪɚɩɪɢɤɨɬɨɪɨɣɨɫɭɳɟɫɬɜ
ɩɥ
ɥɹɟɬɫɹɩɪɨɰɟɫɫɩɟɪɟɯɨɞɚɜɟɳɟɫɬɜɚɢɡɬɜɟɪɞɨɝɨɫɨɫɬɨɹɧɢɹɜɠɢɞɤɨɟɋɚɦɵɦɥɟɝ
ɤɨɩɥɚɜɤɢɦɦɟɬɚɥɥɨɦɹɜɥɹɟɬɫɹɪɬɭɬɶT
= –&ɫɚɦɵɣɬɭɝɨɩɥɚɜɤɢɣɦɟɬɚɥɥ–
ɩɥ
7
ɜɨɥɶɮɪɚɦT
ɝɨɩɥɚɜɤɢɦɢɫT
&ɆɟɬɚɥɥɵɫT
ɩɥ
ɦɟɧɶɲɟ&– ɧɢɡɤɨɩɥɚɜɤɢɦɢ
ɩɥ
ɩɥ
ɛɨɥɶɲɟ&ɭɫɥɨɜɧɨɫɱɢɬɚɸɬɫɹɬɭ
ɍɤɚɡɚɧɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɞɟɥɚɸɬ ɦɟɬɚɥɥɵ ɧɟɡɚɦɟɧɢ
ɦɵɦɢ ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɦɢ ɦɚɬɟɪɢɚɥɚɦɢ ɫɨɟɞɢɧɹɸɳɢɦɢ ɜ ɫɟɛɟ ɩɪɨɱɧɨɫɬɶ ɢ
ɩɥɚɫɬɢɱɧɨɫɬɶ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɮɨɪɦɨɨɛɪɚɡɨɜɚɧɢɹ ɞɟɬɚɥɟɣ ɭɡɥɨɜ ɦɚɲɢɧ ɢ
ɤɨɧɫɬɪɭɤɰɢɣɨɬɥɢɜɤɚɫɜɚɪɤɚɲɬɚɦɩɨɜɤɚɪɟɡɚɧɢɟɢɬɞɫɨɡɞɚɧɢɹɫɩɥɚɜɨɜɢ
ɤɨɦɩɨɡɢɰɢɨɧɧɵɯɦɚɬɟɪɢɚɥɨɜ
Ʉɪɢɫɬɚɥɥɢɱɟɫɤɢɟɫɬɪɭɤɬɭɪɵɦɟɬɚɥɥɨɜ
Ɇɧɨɝɨɟɨɫɜɨɣɫɬɜɚɯɦɟɬɚɥɥɨɜɢɢɯɫɩɥɚɜɨɜɦɨɠɧɨɫɤɚɡɚɬɶɡɧɚɹɫɬɪɭɤɬɭɪɭ
ɢɯɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯɪɟɲɺɬɨɤɄɪɨɦɟɬɨɝɨɜɫɬɪɨɟɧɢɢɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯɪɟɲɺɬɨɤ
ɦɟɬɚɥɥɨɜɧɚɛɥɸɞɚɸɬɫɹɨɛɳɢɟɡɚɤɨɧɨɦɟɪɧɨɫɬɢɤɨɬɨɪɵɟɨɬɥɢɱɚɸɬɢɯ ɨɬɧɟɦɟ
ɬɚɥɥɨɜ
1.3.Ɉɫɨɛɟɧɧɨɫɬɢɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨɫɨɫɬɨɹɧɢɹɜɟɳɟɫɬɜɚ
Ʉɪɢɫɬɚɥɥɨɦ ɧɚɡɵɜɚɟɬɫɹ ɬɜɺɪɞɨɟ ɬɟɥɨ ɨɝɪɚɧɢɱɟɧɧɨɟ ɩɥɨɫɤɢɦɢ ɝɪɚɧɹɦɢ
ɩɟɪɟɫɟɤɚɸɳɢɦɢɫɹɩɨɞɨɩɪɟɞɟɥɺɧɧɵɦɢɭɝɥɚɦɢ
ɍɫɬɚɧɨɜɥɟɧɨɱɬɨɨɝɪɚɧɤɚɹɜɥɹɟɬɫɹɥɢɲɶɫɥɟɞɫɬɜɢɟɦɫɬɪɨɝɨɝɨɩɨɪɹɞɤɚ
ɪɚɫɩɨɥɨɠɟɧɢɹ ɚɬɨɦɨɜ ɫɥɚɝɚɸɳɢɯɦɢɧɟɪɚɥɢ ɩɨɧɹɬɢɟ ©ɤɪɢɫɬɚɥɥª ɩɟɪɟɲɥɨ ɧɚ
ɜɫɟɦɢɧɟɪɚɥɵɢɬɜɟɪɞɵɟɬɟɥɚɫɨɫɬɪɨɝɨɭɩɨɪɹɞɨɱɟɧɧɵɦɪɚɫɩɨɥɨɠɟɧɢɟɦɚɬɨɦɨɜ
Ɉɤɚɡɚɥɨɫɶɱɬɨɧɟɬɨɥɶɤɨɜɧɟɲɧɹɹɨɝɪɚɧɤɚɤɨɬɨɪɚɹɦɨɠɟɬɨɬɫɭɬɫɬɜɨɜɚɬɶɧɨɢ
ɛɨɥɶɲɢɧɫɬɜɨ ɮɢɡɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɨɛɭɫɥɨɜɥɟɧɵ ɯɚɪɚɤɬɟɪɨɦ ɜɡɚɢɦɧɨɝɨɪɚɫɩɨ
ɥɨɠɟɧɢɹɚɬɨɦɨɜɨɛɪɚɡɭɸɳɢɯɤɪɢɫɬɚɥɥɬɟɟɝɨɫɬɪɭɤɬɭɪɨɣ
Ʉɪɢɫɬɚɥɥɩɨɫɬɪɨɟɧɢɡɦɧɨɠɟɫɬɜɚ ɢɨɧɨɜɚɬɨɦɨɜɢɥɢɦɨɥɟɤɭɥ ɉɪɚɜɢɥɶɧɚɹ
ɜɧɟɲɧɹɹɦɨɪɮɨɥɨɝɢɹɨɡɧɚɱɚɟɬ ɱɬɨɤɪɢɫɬɚɥɥ ɨɛɪɚɡɭɟɬɫɹ ɢɡ ɧɟɛɨɥɶɲɢɯɚɝɪɟɝɚ
ɬɨɜɤɨɬɨɪɵɟɫɚɦɢ ɫɢɦɦɟɬɪɢɱɧɵɗɬɢɨɫɧɨɜɧɵɟɚɝɪɟɝɚɬɵɛɥɨɤɢ ɤɨɬɨɪɵɟɫɨ
ɞɟɪɠɚɬɧɟɫɤɨɥɶɤɨɚɬɨɦɨɜ ɢɥɢ ɦɨɥɟɤɭɥ ɧɚɡɵɜɚɸɬɫɹ ɷɥɟɦɟɧɬɚɪɧɵɦɢɹɱɟɣɤɚɦɢ
ɪɟɲɺɬɤɢɆɨɠɧɨɩɨɤɚɡɚɬɶɱɬɨɦɨɪɮɨɥɨɝɢɹɤɪɢɫɬɚɥɥɚɨɛɭɫɥɨɜɥɟɧɚɫɢɦɦɟɬɪɢɟɣ
ɷɥɟɦɟɧɬɚɪɧɵɯɹɱɟɟɤɆɨɪɮɨɥɨɝɢɹɡɚɜɢɫɢɬɨɬɫɤɨɪɨɫɬɢɪɨɫɬɚɪɚɡɧɵɯɝɪɚɧɟɣɧɨ
ɨɫɧɨɜɧɚɹɫɬɪɭɤɬɭɪɚɷɥɟɦɟɧɬɚɪɧɨɣɹɱɟɣɤɢɨɞɧɚɢɬɚɠɟ
Ɉɬɦɟɬɢɦɨɫɨɛɟɧɧɨɫɬɢɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨɫɨɫɬɨɹɧɢɹɜɟɳɟɫɬɜɚ
1. Ɉɞɧɚɢɡɨɫɨɛɟɧɧɨɫɬɟɣɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨɫɨɫɬɨɹɧɢɹɜɟɳɟɫɬɜɚɡɚɤɥɸɱɚɟɬ
ɫɹɜ ɚɧɢɡɨɬɪɨɩɢɢ ɫɜɨɣɫɬɜ. ɋɭɳɧɨɫɬɶ ɚɧɢɡɨɬɪɨɩɢɢɫɨɫɬɨɢɬ ɜ ɬɨɦ ɱɬɨ ɦɧɨɝɢɟ
ɫɜɨɣɫɬɜɚ ɤɪɢɫɬɚɥɥɨɜ ɦɟɯɚɧɢɱɟɫɤɢɟ ɨɩɬɢɱɟɫɤɢɟ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɦɚɝɧɢɬɧɵɟ ɢ
ɞɪɡɚɜɢɫɹɬɨɬɧɚɩɪɚɜɥɟɧɢɹɢɯɢɡɦɟɪɟɧɢɹȺɦɨɪɮɧɵɟɬɟɥɚɢɡɨɬɪɨɩɧɵɢɯɫɜɨɣ
ɫɬɜɚɨɞɢɧɚɤɨɜɵɜɥɸɛɨɦɧɚɩɪɚɜɥɟɧɢɢɜɧɭɬɪɢɞɚɧɧɨɝɨɬɟɥɚ
8
ɉɟɪɟɯɨɞɢɡɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨɫɨɫɬɨɹɧɢɹɜɠɢɞɤɨɟɫɨɫɬɨɹɧɢɟɨɫɭɳɟɫɬɜ
ɥɹɟɬɫɹɫɤɚɱɤɨɨɛɪɚɡɧɨ ɩɪɢɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɧɚɡɵɜɚɟɦɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ
ɩɥɚɜɥɟɧɢɹɉɪɢɷɬɨɦɩɪɨɢɫɯɨɞɢɬɢɫɤɚɱɤɨɨɛɪɚɡɧɨɟɢɡɦɟɧɟɧɢɟɫɜɨɣɫɬɜ
Ɉɞɧɢɦɢɡɫɚɦɵɯɜɚɠɧɵɯɫɜɨɣɫɬɜɤɪɢɫɬɚɥɥɨɜɹɜɥɹɟɬɫɹɬɪɟɯɦɟɪɧɚɹɩɟɪɢ
ɨɞɢɱɧɨɫɬɶɜɢɯɫɬɪɨɟɧɢɢɑɚɫɬɢɰɵɢɡɤɨɬɨɪɵɯɫɨɫɬɨɹɬɤɪɢɫɬɚɥɥɵɪɚɫɩɨɥɨɠɟ
ɧɵɪɟɝɭɥɹɪɧɨɜɩɪɨɫɬɪɚɧɫɬɜɟɢɨɛɪɚɡɭɸɬɤɪɢɫɬɚɥɥɢɱɟɫɤɭɸɪɟɲɺɬɤɭ.
Ʉɪɢɫɬɚɥɥɢɱɟɫɤɚɹɪɟɲɺɬɤɚ – ɩɪɢɫɭɳɟɟɤɪɢɫɬɚɥɥɭɩɟɪɢɨɞɢɱɟɫɤɢɩɨɜɬɨɪɹ
ɸɳɟɟɫɹɜɬɪɺɯɧɚɩɪɚɜɥɟɧɢɹɯɩɪɚɜɢɥɶɧɨɟɪɚɫɩɨɥɨɠɟɧɢɟɱɚɫɬɢɰɚɬɨɦɨɜɢɨɧɨɜ
ɦɨɥɟɤɭɥ
Ʉɪɢɫɬɚɥɥɢɱɟɫɤɢɟɪɟɲɺɬɤɢɦɨɠɧɨɨɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶɞɜɭɦɹɫɩɨɫɨɛɚɦɢ
ɩɨɯɚɪɚɤɬɟɪɭɪɚɫɩɪɟɞɟɥɟɧɢɹɱɚɫɬɢɰɜɩɪɨɫɬɪɚɧɫɬɜɟɩɨɫɩɨɫɨɛɭɭɩɚɤɨɜ
ɤɢ
ɩɨ ɩɪɢɪɨɞɟɯɢɦɢɱɟɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɱɚɫɬɢɰɚɦɢ ɡɚɧɢɦɚɸ
ɳɢɦɢɭɡɥɵɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣɪɟɲɺɬɤɢ
1.3Ʉɪɢɫɬɚɥɥɢɱɟɫɤɢɟɪɟɲɺɬɤɢɢɷɥɟɦɟɧɬɚɪɧɵɟɹɱɟɣɤɢ
ɗɥɟɦɟɧɬɚɪɧɚɹɹɱɟɣɤɚ – ɷɬɨɧɚɢɦɟɧɶɲɢɣɨɛɴɺɦɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣɪɟɲɺɬɤɢ
ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɝɨ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɦɵɫɥɟɧɧɨ ɜɫɸ ɫɬɪɭɤɬɭɪɭ ɤɪɢɫɬɚɥɥɚ
ɩɭɬɺɦɬɪɚɧɫɥɹɰɢɢɹɱɟɣɤɢɜɬɪɺɯɧɚɩɪɚɜɥɟɧɢɹɯ
ɋɬɪɨɟɧɢɟ ɷɥɟɦɟɧɬɚɪɧɨɣ ɹɱɟɣɤɢ ɢɧɞɢɜɢɞɭɚɥɶɧɨ ɞɥɹɤɚɠɞɨɝɨɤɪɢɫɬɚɥɥɢɱɟ
ɫɤɨɝɨɜɟɳɟɫɬɜɚȾɥɹɨɩɢɫɚɧɢɹɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣɪɟɲɺɬɤɢɞɨɫɬɚɬɨɱɧɨɡɧɚɬɶɪɚɫ
ɩɨɥɨɠɟɧɢɟɱɚɫɬɢɰɜɷɥɟɦɟɧɬɚɪɧɨɣɹɱɟɣɤɟɤɨɬɨɪɚɹɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹɟɺɩɚɪɚɦɟɬ
ɪɚɦɢ
ɉɚɪɚɦɟɬɪɚɦɢɷɥɟɦɟɧɬɚɪɧɨɣ ɹɱɟɣɤɢ ɹɜɥɹɸɬɫɹɞɥɢɧɧɵɟɺɪɺɛɟɪ– ɩɟɪɢɨɞɵ
ɢɞɟɧɬɢɱɧɨɫɬɢ ɢɥɢ ɩɟɪɢɨɞɵ ɪɟɲɺɬɤɢ a b c ɢ ɭɝɥɵ ɦɟɠɞɭ ɪɺɛɪɚɦɢ
D
EJ
ɪɢɫ1.2).
Ɋɢɫ1.2ɉɚɪɚɦɟɬɪɵɷɥɟɦɟɧɬɚɪɧɨɣɹɱɟɣɤɢ
9
ɈȻɪɚɜɷɜɝɩɨɤɚɡɚɥɱɬɨɜɫɺɦɧɨɝɨɨɛɪɚɡɢɟɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯɫɬɪɭɤɬɭɪ
ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɫ ɩɨɦɨɳɶɸ ɬɢɩɨɜ ɪɟɲɺɬɨɤ ɨɬɥɢɱɚɸɳɢɯɫɹɩɨ ɮɨɪɦɚɦ ɷɥɟ
ɦɟɧɬɚɪɧɵɯɹɱɟɟɤɢɩɨɫɢɦɦɟɬɪɢɢɗɬɢɪɟɲɺɬɤɢɛɵɥɢɧɚɡɜɚɧɵɪɟɲɺɬɤɚɦɢ
Ȼɪɚɜɷɨɧɢɩɨɞɪɚɡɞɟɥɹɸɬɫɹɧɚɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɢɯɫɢɫɬɟɦɫɢɧɝɨɧɢɣ).
ȼɬɚɛɥ1.2 ɭɤɚɡɚɧɵɩɚɪɚɦɟɬɪɵɤɨɬɨɪɵɟɨɩɪɟɞɟɥɹɸɬɷɥɟɦɟɧɬɚɪɧɭɸɹɱɟɣɤɭ
ɞɥɹɤɚɠɞɨɣɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɨɣɫɢɫɬɟɦɵ ɚ ɧɚɪɢɫ1.3 ɩɪɟɞɫɬɚɜɥɟɧɵ ɜɫɟ
ɪɟɲɺɬɨɤȻɪɚɜɷ.
Ɍɚɛɥɢɰɚ1.2
ɉɚɪɚɦɟɬɪɵɤɨɬɨɪɵɟɨɩɪɟɞɟɥɹɸɬɷɥɟɦɟɧɬɚɪɧɭɸɹɱɟɣɤɭ
ɞɥɹɤɚɠɞɨɣɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɨɣɫɢɫɬɟɦɵ
Ʉɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɚɹɫɢɫɬɟɦɚ
ɉɚɪɚɦɟɬɪɵɷɥɟɦɟɧɬɚɪɧɨɣ
ɹɱɟɣɤɢ
ɤɭɛɢɱɟɫɤɚɹ D E FĮ ȕ Ȗ 90°
ɬɟɬɪɚɝɨɧɚɥɶɧɚɹ D EFĮ ȕ Ȗ 90°
ɪɨɦɛɢɱɟɫɤɚɹ DEFĮ ȕ Ȗ 90°
ɝɟɤɫɚɝɨɧɚɥɶɧɚɹ D EFĮ ȕ Ȗ 120°
ɬɪɢɝɨɧɚɥɶɧɚɹ
1) D EFĮ ȕ Ȗ 120°;
2) a=b=c, Į ȕ Ȗ90°
ɦɨɧɨɤɥɢɧɧɚɹ DEFĮ Ȗ ȕ90°
ɬɪɢɤɥɢɧɧɚɹ DEFĮȕȖ90°
Ɋɟɲɺɬɤɢɫɭɡɥɚɦɢɬɨɥɶɤɨɜɭɝɥɚɯɧɚɡɵɜɚɸɬɩɪɢɦɢɬɢɜɧɵɦɢ (Ɋɤɨɝɞɚɭɡɟɥ
ɧɚɯɨɞɢɬɫɹɜɰɟɧɬɪɟɪɟɲɺɬɤɢɧɚɡɵɜɚɸɬɫɹɨɛɴɺɦɧɨɰɟɧɬɪɢɪɨɜɚɧɧɵɦɢ (Iɤɨɝɞɚ
ɪɟɲɺɬɤɢɫɨɞɟɪɠɚɬɚɬɨɦɧɚɝɪɚɧɹɯɨɧɢɧɚɡɵɜɚɸɬɫɹɝɪɚɧɟɰɟɧɬɪɢɪɨɜɚɧɧɵɦɢ(F).
ɪɟɲɺɬɨɤ Ȼɪɚɜɷ ɫɨɫɬɚɜɥɹɸɬ ɝɪɭɩɩ ɩɪɟɞɫɬɚɜɥɟɧɧɚɹ ɤɚɠɞɚɹ ɩɪɢɦɢɬɢɜɧɨɣ
ɪɟɲɺɬɤɨɣɢɷɬɢɩɪɚɜɢɥɶɧɵɟɮɢɝɭɪɵɬɨɱɧɨɬɚɤɢɟɠɟɤɚɤɢɟɫɨɨɬɜɟɬɫɬɜɭɸɬɤɪɢ
ɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɢɦɫɢɫɬɟɦɚɦɌɚɤɢɦɨɛɪɚɡɨɦɩɟɪɜɚɹɯɚɪɚɤɬɟɪɧɚɹɨɫɨɛɟɧɧɨɫɬɶ
ɫɬɪɨɟɧɢɹ ɤɪɢɫɬɚɥɥɨɜ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ ɱɬɨ ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɢɯ ɫɢɫɬɟɦ
ɨɬɪɚɠɚɸɬɫɭɳɟɫɬɜɨɜɚɧɢɟɫɟɦɢ ɩɪɚɜɢɥɶɧɵɯ ɮɨɪɦɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶɩɥɨɬɧɨ
ɭɩɚɤɨɜɚɧɵɢɡɚɩɨɥɧɹɸɬɩɪɨɫɬɪɚɧɫɬɜɨ
ɂɡɜɢɡɭɚɥɶɧɵɯɧɚɛɥɸɞɟɧɢɣɦɨɪɮɨɥɨɝɢɢɤɪɢɫɬɚɥɥɚɦɵɦɨɠɟɦɭɫɬɚɧɨɜɢɬɶ
ɫɢɦɦɟɬɪɢɸɷɥɟɦɟɧɬɚɪɧɨɣɹɱɟɣɤɢ ɢɫɩɨɫɨɛ ɤɚɤɢɦ ɭɩɚɤɨɜɚɧɵɦɨɥɟɤɭɥɵɨɛɪɚ
ɡɭɸɳɢɟ ɤɪɢɫɬɚɥɥ Ɉɞɧɚɤɨ ɞɟɣɫɬɜɢɬɟɥɶɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ ɚɬɨɦɨɜ ɟɳɺ ɧɟɥɶɡɹ
ɨɩɪɟɞɟɥɢɬɶ
10
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