KOMPTON SOCHILISHINI SODDALASHTIRIB TUSHUNTIRISH: FOTON VA ELEKTRONNI ZARRACHA SIFATIDA MODELLASHTIRISH USULI

Аннотация

Compton scattering is the phenomenon in which high-energy photons collide with free electrons, resulting in an increase in the photons’ wavelength. Traditionally, this effect is explained through the laws of quantum mechanics— specifically, by applying the conservation of momentum and energy between photons and electrons. Due to the abstract and conceptually complex nature of this explanation, many students find it difficult to grasp. This study proposes a simplified method for explaining the Compton effect by modeling the photon and electron as particles. In this approach, the photon is visualized as a small-mass particle that 135 International scientific journal “Interpretation and researches” Volume 1 issue 7 (53) | ISSN: 2181-4163 | Impact Factor: 8.2 strikes an electron, analogous to a ball hitting another object, thereby illustrating the exchange of energy and momentum in a more tangible way. This analogy, which likens the decrease in the scattered photon's energy and the corresponding increase in wavelength to a classical elastic collision, facilitates student understanding. By incorporating visual and intuitive representations, this method has the potential to enhance teaching effectiveness and learning outcomes in physics education. Keywords: Compton scattering, Photon-electron collision, Wavelength shift, Intuitive understanding in physics, Educational effectiveness Kompton sochilishi — 1923-yilda Artur Kompton tomonidan kashf etilgan, yuqori energiyali elektromagnit nurlanish (odatda rentgen yoki gamma nurlari) elektronlar bilan to‘qnashganda ularning to‘lqin uzunligi o‘zgarishiga olib keladigan hodisadir. Bu tajriba klassik elektromagnit nazariyadan tashqari tushuntirishni talab qilgan va foton zarracha modeli g‘oyasini mustahkamlab bergan. Fotonning boshlang'ich yo'nalishi boshlang'ich to'lqin uzunligi λ bilan ifodalanadi. Sochilishdan keyin fotonning yo‘nalishi to'lqin uzunligi λ′ ga o'zgaradi, bu esa fotonning energiyasining kamayishini anglatadi. Elektronning boshlang'ich holati tinch holatdagi zarracha sifatida ko'riladi. Sochilishdan keyin elektron harakati boshlanadi, uning kinetik energiyasi foton energiyasining kamayishi orqali o'zgaradi. Elektronning yo'nalishi fotonning sochilish burchagiga qarab o'zgaradi. 90° burchagida fotonning energiyasi maksimal kamayadi va elektron maksimal tezlikda harakatlanadi. Kvant mexanikasiga ko‘ra, foton va elektron to‘qnashganda energiya va impuls saqlanish qonunlariga amal qilinadi. Ushbu jarayon quyidagi formulalar bilan ifodalanadi: Energiyaning saqlanishi √( ) ( ) Impulsning saqlanishi (vektor shaklda): ⃗⃗⃗⃗ ⃗⃗⃗⃗ ⃗⃗⃗⃗ Kompton formulasiga kelinadi: ( ) Bu yerda: - boshlang‘ich to‘lqin uzunligi - sochilgan fotonning to‘lqin uzunligi - sochilish burchagi - Komptom to‘lqin uzunligi Talabalar bu formulalarni eslab qolishlari mumkin, ammo fizik mazmunini tushunishlari ko‘pincha murakkab bo‘ladi. Kompton effektini soddalashtirib tushuntirish uchun biz fotonni kichik massali, energiyali to‘p, elektronni esa katta massali, tinch holatdagi to‘p sifatida tasavvur qilamiz. Bu ikki zarra bir-biriga urilganda kichik to‘p (foton) katta to‘pga (elektron) 136 International scientific journal “Interpretation and researches” Volume 1 issue 7 (53) | ISSN: 2181-4163 | Impact Factor: 8.2 zarba beradi va natijada yo‘nalishi o‘zgaradi hamda tezligi kamayadi. Bu — fotonning energiyasi kamayib, to‘lqin uzunligi ortishiga teng keladi. Bu model orqali talabalar: Fotonning "zarba" berish xususiyatini Energiyaning almashinishini Sochilish burchagining natijaviy ta’sirini intuitiv tushunishadi.[1-10] Matematik modellashtrish va hisoblash Dastlabki shartlar: Fotonning boshlang‘ich to‘lqin uzunligi λ=0.071 nm=7.1×10−11 m, (bu 17.5 keV energiyali rentgen fotoniga mos keladi). Sochilish burchagi Elektron - tinch holatdagi zarracha ( m =9.11×10−31 kg). e Kompton formulasi asosida hisoblash: ( ) ( ) Shunday qilib: Foton energiyasining kamayishini hisoblash: Foton energiyasi: Boshlang‘ich energiya: Sochilgan foton energiyasi: Demak, foton energiyasining bir qismi elektronning kinetik energiyasiga aylangan. Modellashtirish asosida grafik chizma: Biz grafik chizmada quyidagilarni ko‘rsatamiz: To‘lqin uzunligining burchakka bog‘liqligi: Δλ=f(θ) Energiya kamayishi grafigi: E=f(θ) Foton yo‘nalishi oldin va keyin Elektronning harakat yo‘nalishi va energiyasi 137 International scientific journal “Interpretation and researches” Volume 1 issue 7 (53) | ISSN: 2181-4163 | Impact Factor: 8.2 Yuqoridagi grafiklarda: 1. Δλ (to‘lqin uzunligining o‘zgarishi) – sochilish burchagi oshgani sayin oshadi, bu Kompton effekti xususiyatidir. 2. Sochilgan foton energiyasi (E′) – burchak ortishi bilan kamayadi, chunki energiyaning bir qismi elektron kinetik energiyasiga o‘tadi. Kompton sochilishi kvant fizikasi uchun asosiy hodisalardan biri bo‘lib, unda yorug‘likning zarracha xossalari yaqqol namoyon bo‘ladi. Ushbu hodisa orqali fotonning elektron bilan zarracha kabi to‘qnashib, energiya va impuls almashinuvi