Ihe Nlereanya nke Ajụjụ Mkparịta ụka Compton Mmetụta
Mmetụta Compton bụ ihe dị oke mkpa na nkà mmụta sayensị nke quantum. Nchọpụta a abụghị naanị na ọ na-eme ka nghọta anyị banyere abụọ nke ìhè dịkwuo omimi kamakwa ọ na-enyekwa ihe akaebe siri ike maka ozizi quantum nke radieshon. Isiokwu a ga-enyocha mmetụta Compton, ụkpụrụ ndị bụ isi ya, ma nye ụfọdụ ihe atụ nke nsogbu na ngwọta iji tinye echiche a n'ọrụ.
Ịghọta Mmetụta Compton
Mmetụta Compton, nke aha ya bụ Arthur H. Compton, bụ ihe na-eme ka foton (ihe dị ka obere ìhè) na elektrọn kụọ ma nwee mgbanwe na ogologo ebili mmiri. Mgbe ọ gbasịrị, foton na-ebufe ụfọdụ ike ya na elektrọn, na-eme ka foton ahụ nwee mmụba na ogologo ebili mmiri (ma ọ bụ mbelata na ugboro ole).
A na-akpọ mgbanwe a na ogologo ebili mmiri Compton shift, a pụkwara igosi ya site na nha nhata:
\[
\Delta \lambda = \lambda' – \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Ebe:
– \(\Delta \lambda\) bụ mgbanwe na ogologo ebili mmiri nke foton,
– \(\lambda\) bụ ogologo mbu nke foton,
– \(\lambda'\) bụ ogologo ebili mmiri nke foton mgbe ọ gbasịrị,
– \(h\) bụ ihe Planck na-agbanwe agbanwe (\(6.626 \ugboro 10^{-34} \, \text{Js}\)),
– \(m_e\) bụ oke nke elektrọn (\(9.109 \ugboro 10^{-31} \, \text{kg}\)),
– \(c\) bụ ọsọ nke ìhè (\(3 \u003 10^8 \, \text{m/s}\)),
– \(\theta\) bụ akụkụ nke mgbasa nke foton.
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ajụjụ nke Atọ
Foton nwere ogologo ebili mmiri nke 0,1 nm na-akụ elektrọn na-anaghị agagharị. A na-agbasasị foton ahụ n'akụkụ 90° site na ntụziaka mbụ ya. Gbakọọ ogologo ebili mmiri nke foton ahụ mgbe ọ kụsịrị!
Azịza:
A maara:
– Ogologo ebili mmiri mbụ, \(\lambda = 0.1 \, \text{nm} = 0.1 \times 10^{-9} \, \text{m}\)
– Akụkụ mgbasa ozi, \(\theta = 90^\circ \)
Site na iji usoro mgbanwe Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Dochie ụkpụrụ nke Planck's constant, oke nke elektrọn, na ọsọ nke ìhè:
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{9.109 \ugboro 10^{-31} \ugboro 3 \ugboro 10^8}(1 – \cos 90^\circ)
\]
Ebe ọ bụ na \(\cos 90^\circ = 0\),
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{9.109 \ugboro 10^{-31} \ugboro 3 \ugboro 10^8}
\]
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{2.7327 \ugboro 10^{-22}}
\]
\[
\Delta \lambda = 2.43 \ugboro 10^{-12} \, \text{m} = 0.00243 \, \text{nm}
\]
Ya mere, ogologo ebili mgbe ihe ahụ gasịrị bụ:
\[
\lambda' = \lambda + \Delta \lambda = 0.1 \, \text{nm} + 0.00243 \, \text{nm} = 0.10243 \, \text{nm}
\]
Ajụjụ nke Atọ
A na-agbasasị foton nwere ogologo ebili mmiri \( \lambda = 0.05 \, \text{nm} \) n'akụkụ \( \theta = 120^\circ \). Chọpụta ogologo ebili mmiri nke foton mgbe agbasasịrị.
Azịza:
A maara:
– Ogologo ebili mmiri mbụ, \(\lambda = 0.05 \, \text{nm} = 0.05 \times 10^{-9} \, \text{m}\)
– Akụkụ mgbasa ozi, \(\theta = 120^\circ \)
Site na iji usoro mgbanwe Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Dochie ụkpụrụ nke Planck's constant, oke nke elektrọn, na ọsọ nke ìhè:
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{9.109 \ugboro 10^{-31} \ugboro 3 \ugboro 10^8}(1 – \cos 120^\circ)
\]
Ebe ọ bụ na \(\cos 120^\circ = -0.5\),
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{9.109 \ugboro 10^{-31} \ugboro 3 \ugboro 10^8}(1 – (-0.5))
\]
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{9.109 \ugboro 10^{-31} \ugboro 3 \ugboro 10^8}(1 + 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{2.7327 \ugboro 10^{-22}} \ugboro 1.5
\]
\[
\Delta \lambda = 2.43 \ugboro 10^{-12} \, \text{m} \ugboro 1.5 = 3.645 \ugboro 10^{-12} \, \text{m} = 0.003645 \, \text{nm}
\]
Ya mere, ogologo ebili mgbe ihe ahụ gasịrị bụ:
\[
\lambda' = \lambda + \Delta \lambda = 0.05 \, \text{nm} + 0.003645 \, \text{nm} = 0.053645 \, \text{nm}
\]
Ajụjụ nke Atọ
Ọ bụrụ na ogologo ebili mmiri nke foton mgbe a gbasasịrị ya bụ 0.045 nm ma akụkụ nke ịgbasa ya bụ \(60^\cir\), chọpụta ogologo ebili mmiri nke foton tupu ịgbasa ya.
Azịza:
A maara:
– Ogologo ebili mmiri mgbe ọ gbasasịrị, \(\lambda' = 0.045 \, \text{nm} = 0.045 \times 10^{-9} \, \text{m}\)
– Akụkụ mgbasa ozi, \(\theta = 60^\circ \)
Site na iji usoro mgbanwe Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Dochie ụkpụrụ nke Planck's constant, oke nke elektrọn, na ọsọ nke ìhè:
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{9.109 \ugboro 10^{-31} \ugboro 3 \ugboro 10^8}(1 – \cos 60^\circ)
\]
Ebe ọ bụ na \(\cos 60^\circ = 0.5\),
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{9.109 \ugboro 10^{-31} \ugboro 3 \ugboro 10^8}(1 - 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \ugboro 10^{-34}}{2.7327 \ugboro 10^{-22}} \ugboro 0.5
\]
\[
\Delta \lambda = 2.43 \ugboro 10^{-12} \, \text{m} \ugboro 0.5 = 1.215 \ugboro 10^{-12} \, \text{m} = 0.001215 \, \text{nm}
\]
A maara ogologo ebili mmiri mgbe ihe mberede ahụ gasịrị:
\[
\lambda' = \lambda + \Delta \lambda
\]
Ya mere, ogologo ebili mmiri tupu mgbasa bụ:
\[
\lambda = \lambda' – \Delta \lambda = 0.045 \, \text{nm} – 0.001215 \, \text{nm} = 0.043785 \, \text{nm}
\]
Mmechi
Ịghọta mmetụta Compton na-enye anyị ohere ịghọta nke ọma mmekọrịta dị n'etiti photons na elektrọn n'ihe gbasara physics quantum. Mgbanwe ogologo ebili a n'ihi mgbasa na-egosi okpukpu abụọ nke ìhè ma na-eme ka ozizi quantum nke radieshon sikwuo ike. Ihe atụ ndị dị n'elu bụ ngwa kpọmkwem nke Compton equivalent, nke nwere ike inyere anyị aka ịghọta echiche bụ isi ma gbakọọ mgbanwe ogologo ebili n'okpuru ọnọdụ dị iche iche.
