Cov Lus Nug Piv Txwv Sib Tham Txog Cov Kev Tsis Zoo ntawm Cov Hnyav thiab Lub Zog Sib Koom Tes
Hauv kev kawm txog nuclear physics, cov tswv yim ntawm qhov tsis zoo ntawm lub cev thiab lub zog khi ua lub luag haujlwm tseem ceeb hauv kev nkag siab txog kev ruaj khov ntawm cov nuclei atomic. Qhov tsis zoo ntawm lub cev yog hais txog qhov sib txawv ntawm qhov hnyav tiag tiag ntawm lub nucleus atomic thiab tag nrho qhov hnyav ntawm nws cov protons thiab neutrons. Cov lus txhais no yog los ntawm kev nkag siab tias qee qhov hnyav ploj thaum lub sijhawm tsim lub nucleus, uas tom qab ntawd hloov mus ua lub zog khi raws li lub hauv paus ntsiab lus ntawm qhov sib npaug ntawm lub cev thiab lub zog uas Albert Einstein tau tsim hauv nws cov qauv nto moo, \(E=mc^2\).
Lub zog khi yog qhov ntau ntawm lub zog uas xav tau los faib ib lub nucleus ua cov protons thiab neutrons sib cais. Lub zog khi ntau dua rau ib lub nucleon, lub nucleus ruaj khov dua. Cov hauv qab no yog kev sib tham txog cov teeb meem piv txwv ntsig txog qhov tsis zoo ntawm pawg thiab lub zog khi kom peb nkag siab tob txog lub tswv yim no.
Piv txwv lus nug 1: Xam qhov hnyav tsis zoo
Lo lus nug:
Ib tug tub ntxhais kawm raug hais kom xam qhov hnyav ntawm lub Helium-4 atomic nucleus (\(^4_2He\)), uas muaj 2 protons thiab 2 neutrons. Paub tias qhov hnyav ntawm proton yog 1.007825 u, qhov hnyav ntawm neutron yog 1.008665 u, thiab qhov hnyav ntawm Helium-4 atomic nucleus yog 4.002603 u. Xam qhov hnyav ntawm lub nucleus.
Kev Sib Tham:
1. Txheeb xyuas Tag Nrho Qhov Hnyav ntawm Protons thiab Neutrons:
Tus naj npawb ntawm cov protons = 2, tus naj npawb ntawm neutrons = 2
Tag nrho cov protons = 2 × 1.007825 u = 2.015650 u
Tag nrho cov hnyav ntawm neutrons = 2 × 1.008665 u = 2.017330 u
Yog li, tag nrho cov pawg ntawm protons thiab neutrons yog:
\[
\text{Tag nrho qhov hnyav} = 2.015650 \, \text{u} + 2.017330 \, \text{u} = 4.032980 \, \text{u}
\]
2. Xam Qhov Loj Ntawm Qhov Tsis Zoo:
\[
\text{Qhov hnyav tsis zoo} (\Delta m) = \text{Qhov hnyav tag nrho} - \text{Qhov hnyav ntawm lub nucleus}
\]
\[
\Delta m = 4.032980 \, \text{u} – 4.002603 \, \text{u} = 0.030377 \, \text{u}
\]
Qhov hnyav tsis zoo rau Helium-4 nucleus yog 0.030377 u.
Piv Txwv Lo Lus Nug 2: Xam Lub Zog Sib Koom Tes
Lo lus nug:
Siv qhov teeb meem loj ntawm qhov teeb meem piv txwv thawj zaug, xam lub zog khi ntawm Helium-4 nucleus. (Muab: 1 u = 931.5 MeV/c²)
Kev Sib Tham:
1. Hloov Qhov Loj Me Me mus rau Zog:
Lub zog khi (\(E\)) yog xam los ntawm kev siv tus qauv \(E = \Delta m \times c^2\). Ntawm no, \(c^2\) hauv cov chav siv feem ntau ntawm MeV/u yog 931.5 MeV/u.
\[
E = 0.030377 \, \text{u} \times 931.5 \, \text{MeV/u}
\]
\[
E = 28.299 \, \text{MeV}
\]
Lub zog khi ntawm Helium-4 nucleus yog 28.299 MeV.
2. Xam Lub Zog Sib Koom Tes Ib Lub Nucleon:
Helium-4 muaj tag nrho 4 lub nucleons (2 protons thiab 2 neutrons). Yuav kom nrhiav tau lub zog khi rau ib lub nucleon, peb faib tag nrho lub zog khi los ntawm tus naj npawb ntawm cov nucleons:
\[
\text{Lub zog khi rau ib nucleon} = \frac{28.299 \, \text{MeV}}{4} = 7.075 \, \text{MeV/nucleon}
\]
Cov Ntsiab Lus Siab Tshaj Plaws
Kev nkag siab txog lub zog khi rau ib lub nucleon yog qhov tseem ceeb rau kev txiav txim siab qhov ruaj khov ntawm lub nuclear; qhov nqi no siab dua, lub nucleus yuav ruaj khov dua. Cov nucleus uas muaj lub zog khi siab rau ib lub nucleon feem ntau yuav tiv taus cov tshuaj tiv thaiv xws li fission lossis fusion.
Piv txwv lus nug 3: Kev sib piv ntawm lub zog khi
Lo lus nug:
Piv lub zog khi rau ib lub nucleon rau ob lub nuclei atomic hauv qab no: Deuterium (\(^2_1H\)) nrog lub nuclear mass ntawm 2.014102 u thiab Helium-4 los ntawm qhov piv txwv dhau los, thiab xam qhov sib txawv. Lub mass ntawm proton yog 1.007825 u thiab lub mass ntawm neutron yog 1.008665 u.
Kev Sib Tham:
1. Deuterium (\(^2_1H\)):
- Tag Nrho Qhov Hnyav ntawm Protons thiab Neutrons:
Tag nrho qhov hnyav = 1 × 1.007825 u + 1 × 1.008665 u = 2.016490 u
- Deuterium Mass Defect:
\[
\Delta m = 2.016490 \, \text{u} – 2.014102 \, \text{u} = 0.002388 \, \text{u}
\]
- Deuterium Binding Zog:
\[
E = 0.002388 \, \text{u} \times 931.5 \, \text{MeV/u} = 2.223 \, \text{MeV}
\]
- Lub zog khi rau ib Deuterium Nucleon:
Vim tias Deuterium muaj 2 nucleons (1 proton thiab 1 neutron),
\[
\frac{2.223 \, \text{MeV}}{2} = 1.1115 \, \text{MeV/nucleon}
\]
2. Kev Sib Piv thiab Xaus Lus:
Lub zog khi rau ib lub nucleon ntawm Helium-4: 7.075 MeV/nucleon
Lub zog khi rau ib nucleon ntawm Deuterium: 1.1115 MeV/nucleon
Qhov txawv:
\[
7.075 \, \text{MeV/nucleon} – 1.1115 \, \text{MeV/nucleon} = 5.9635 \, \text{MeV/nucleon}
\]
Los ntawm qhov kev sib piv no, peb tuaj yeem pom tias Helium-4 ruaj khov dua li Deuterium, raws li qhia los ntawm nws lub zog khi siab dua ib lub nucleon.
Xaus
Kev nkag siab txog qhov tsis zoo ntawm cov pawg thiab lub zog khi yog qhov tseem ceeb hauv kev tshawb fawb txog nuclear thiab muab kev nkag siab txog kev ruaj khov ntawm nuclear. Los ntawm kev xam lub zog khi, peb tuaj yeem kwv yees qhov kev ua haujlwm thiab kev ruaj khov ntawm qee cov isotopes. Cov tswv yim no tsis yog tsuas yog qhov tseem ceeb rau kev tshawb fawb theoretical xwb tab sis kuj muaj kev siv tau, suav nrog kev tsim hluav taws xob nuclear thiab kev tshawb fawb astrophysical. Los ntawm kev xyaum cov teeb meem zoo li cov saum toj no, peb lub peev xwm los nkag siab thiab siv cov tswv yim nyuaj no yuav txhim kho.
