Ajụjụ Ihe Nlereanya Na-atụle Echiche Ọnụọgụgụ Planck
Echiche Quantum nke Planck bụ mgbanwe dị mkpa na fiziki nke oge a, na-agbanwe nghọta anyị gbasara radieshon anụ ojii na usoro nhazi quantum. Max Planck webatara ozizi a na 1900, na-enyere aka ịkọwa ihe ndị na-eme na fiziki oge ochie enweghị ike ịkọwa. Isiokwu a ga-enyocha ozizi quantum nke Planck site na mkparịta ụka nke ihe atụ nsogbu, site na echiche ndị bụ isi ruo na ojiji.
Ndabere na Ozizi Quantum nke Planck
Tupu anyị ekwuo maka nsogbu ihe atụ a, ọ dị mkpa ịghọta ihe ndabere nke ozizi Planck nke Quantum. Na ngwụcha narị afọ nke 19, physics oge gboo chere nnukwu ihe ịma aka ihu n'ịkọwa ụdị radieshọn nke ahụ ojii. Radieshọn nke ahụ ojii bụ radieshọn electromagnetic nke ihe na-ewepụta n'otu okpomọkụ kpọmkwem.
Fizik ochie, site na iji iwu Rayleigh-Jeans, buru amụma na ike radieshon ga-abawanye nke ukwuu na ugboro ole dị elu, nke a maara dị ka "ọdachi ultraviolet." Nke a bụ ebe Max Planck wepụtara ngwọta mgbanwe: o kwuru na ike na-apụta ma ọ bụ na-abanye na ngwugwu dị iche iche a na-akpọ "quanta."
Usoro Isi nke Atụmatụ Quantum nke Planck
Usoro bụ isi nke ike kwantum dịka ozizi Planck si dị bụ:
\[ E = h \nu \]
Ebe:
– \( E \) bụ ike nke ngwugwu quantum (a na-akpọkwa quanta),
– \(h \) bụ ihe Planck na-agbanwe agbanwe (\(6.626 \ugboro 10^{-34} \, \text{Js}\)),
– \( \nu \) bụ ugboro ole radieshọn na-apụta.
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ajụjụ nke 1: Ngụkọta Ike Kwatum
Ajụjụ:
Foton nwere ugboro nke \( ugboro 5 10^{14} \, \text{Hz} \). Gbakọọ ike nke foton dịka ozizi Planck si dị.
Azịza:
A maara:
– Ugboro ugboro \( \nu = 5 \ugboro 10^{14} \, \text{Hz} \)
– Planck's na-agbanwe agbanwe \( h = 6.626 \ugboro 10^{-34} \, \text{Js} \)
Site na iji usoro ike kwantum nke Planck:
\[ E = h \nu \]
\[ E = (6.626 \ugboro 10^{-34} \, \text{Js}) \ugboro (ugboro ise 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \ugboro 10^{-19} \, \ederede{J} \]
Ya mere, ike nke foton bụ \( 3.313 \ugboro 10^{-19} \, \text{J} \).
Ajụjụ nke Abụọ: Mmekọrịta dị n'etiti ogologo ebili mmiri na ike
Ajụjụ:
Chọpụta ike nke foton nke nwere ogologo ebili mmiri nke \( 600 \, \text{nm} \).
Azịza:
A maara:
– Ogologo Wave \( \lambda = 600 \, \text{nm} = 600 \ugboro 10^{-9} \, \text{m} \)
– Ọsọ nke ìhè \( c = ugboro 3 10^{8} \, \text{m/s} \)
– Planck's na-agbanwe agbanwe \( h = 6.626 \ugboro 10^{-34} \, \text{Js} \)
Nke mbụ, anyị kwesịrị ịchọta ugboro ole \( \nu \) site na iji mmekọrịta dị n'etiti ogologo ebili mmiri na ugboro ole:
\[ \nu = \frac{c}{\lambda} \]
\[ \nu = \frac{3 \ugboro 10^{8} \, \text{m/s}}{600 \ugboro 10^{-9} \, \text{m}} \]
\[ \nu = ugboro ise 10^{14} \, \ederede{Hz} \]
Ugbu a, anyị nwere ike iji usoro ike kwantum nke Planck:
\[ E = h \nu \]
\[ E = (6.626 \ugboro 10^{-34} \, \text{Js}) \ugboro (ugboro ise 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \ugboro 10^{-19} \, \ederede{J} \]
Ya mere, ike nke foton nwere ogologo ebili mmiri \(600 \, \text{nm} \) bụ \( 3.313 \times 10^{-19} \, \text{J} \).
Ajụjụ nke Atọ: Ike nke ejikọtara ya na Radiation nke Ahụ Ojii
Ajụjụ:
Ahụ ojii dị n'okpomọkụ nke 3000 K. Kedu ugboro ole radieshon kacha elu nke ihe ahụ na-emepụta?
Azịza:
A maara:
– Okpomọkụ \( T = 3000 \, \ederede{K} \)
– Boltzmann's constant \( k = 1.38 \ugboro 10^{-23} \, \text{J/K} \)
Dịka iwu Wien si kwuo, a na-enye radieshon ahụ ojii n'ogologo ogologo oge \( \lambda_{\text{max}} \) site na:
\[ \lambda_{\text{max}} T = 2.898 \ugboro 10^{-3} \, \text{m K} \]
Ka ọ were:
\[ \lambda_{\text{max}} = \frac{2.898 \ugboro 10^{-3} \, \text{m K}}{3000 \, \text{K}} \]
\[ \lambda_{\text{max}} = 9.66 \ugboro 10^{-7} \, \text{m} \]
Iji chọta ugboro kacha elu \( \nu_{\text{max}} \), anyị na-eji:
\[ \nu_{\text{max}} = \frac{c}{\lambda_{\text{max}}} \]
\[ \nu_{\text{max}} = \frac{3 \ugboro 10^{8} \, \text{m/s}}{9.66 \ugboro 10^{-7} \, \text{m}} \]
\[ \nu_{\text{max}} \ihe dị ka 3.10 \ugboro 10^{14} \, \text{Hz} \]
Ya mere, ugboro kachasị elu nke radieshon nke ahụ ojii na-emepụta na okpomọkụ nke 3000 K bụ ihe dị ka \( 3.10 \ugboro 10^{14} \, \text{Hz} \).
Ajụjụ nke 4: Nkesa nke Ike Radiation
Ajụjụ:
Gbakọọ ike zuru oke nke ahụ ojii na-ewepụta n'otu mpaghara elu na okpomọkụ nke 5000 K.
Azịza:
A maara:
– Okpomọkụ \( T = 5000 \, \ederede{K} \)
– Stefan-Boltzmann na-agbanwe agbanwe \( \sigma = 5.67 \ugboro 10^{-8} \, \text{W/m}^2\text{K}^4 \)
Usoro maka nkesa nke ike radieshọn zuru oke nke ahụ ojii na-ewepụta bụ:
\[ E = \sigma T^4 \]
\[ E = (5.67 \ugboro 10^{-8} \, \ederede{W/m}^2\ederede{K}^4) \ugboro (5000 \, \ederede{K})^4 \]
\[ E = 5.67 \ugboro 10^{-8} \ugboro 625 \ugboro 10^{12} \]
\[ E \ihe dị ka 3.54375 \ugboro 10^{7} \, \text{W/m}^2 \]
Ya mere, ike zuru oke nke ahụ ojii na-ewepụta na okpomọkụ nke 5000 K bụ \( 3.54375 \ugboro 10^{7} \, \text{W/m}^2 \).
Mmechi
Usoro Quantum nke Planck na-enye ntọala dị mkpa maka fiziki nke oge a, na-aghọta otu esi ewepụta ike ma na-amịkọrọ ya n'ụdị quanta. Site na iji usoro bụ isi \( E = h \nu \), anyị nwere ike ịgbakọ ọtụtụ ozi dị mkpa, gụnyere ike nke photon, ugboro ole na ogologo ebili mmiri nke jikọtara ya na radieshon electromagnetic, na nkesa ike nke radieshon sitere na ahụ ojii. Ọmụmụ ihe a abụghị naanị imebi ókè nke fiziki oge ochie kamakwa o meghere ụzọ maka mmepe nke mekaniki quantum na ihe ọhụrụ teknụzụ dị iche iche.
