Nā nīnau hoʻohālike e kūkākūkā ana i ke kumumanaʻo o nā Photons
ʻO nā photons nā ʻāpana mua e hoʻokumu i ke kumu o ke kumumanaʻo quantum o ka mālamalama. Ma ke ʻano he quantum o ka mālamalama, lawe ka photon i kahi pūʻolo ikehu e pili pono ana i kona alapine (frequency). Ua hoʻolauna mua ʻia kēia manaʻo e Albert Einstein i ka makahiki 1905. Ma kēia ʻatikala, e kūkākūkā mākou i kekahi mau laʻana a me nā kūkākūkā e pili ana i nā photons e hoʻomālamalama i ko mākou ʻike ʻana i kēia kumuhana.
Ka Hoʻomaopopo Kumu o nā Photons
ʻO nā photons he mau ʻāpana māmā, a i ʻole quanta, o ka radiation electromagnetic. I loko o ke kumumanaʻo quantum, ʻaʻohe nuipa hoʻomaha o nā photons akā loaʻa iā lākou ka ikehu a me ka momentum. Hiki ke helu ʻia ka ikehu o kahi photon me ka hoʻohana ʻana i ka hoohalike i hoʻomohala ʻia e Max Planck:
\[ E = hf \]
Ma hea:
– ʻO \( E \) ka ikehu photon
– ʻO \( h \) ke kūpaʻa o Planck ( \( 6.626 \times 10^{-34} \) Js)
– ʻO \( f \) ke alapine (frequency) o ke kukui
Hiki ke hōʻike ʻia ka pilina ma waena o ka ikehu photon a me ka nalu lōʻihi \(\lambda\) e ka hoohalike aʻe:
\[ E = \frac{hc}{\lambda} \]
Ma hea:
– ʻO \( c \) ka wikiwiki o ka mālamalama i loko o kahi hakahaka \( (3 \times 10^8 \) m/s)
Nā Nīnau Laʻana a me ke Kūkākūkā
Nīnau 1: Ke helu ʻana i ka ikehu Photon
Nīnau: He 500 nm ka lōʻihi o ka nalu o ka photon. E helu i ka ikehu o ka photon ma nā joules.
Kūkākūkā:
ʻO ka mea mua, hoʻololi mākou i ka nalu mai nā nanometers i nā mika.
\[ 500 \ \text{nm} = 500 \times 10^{-9} \ \text{m} \]
Ke hoʻohana nei i ka hoʻohālikelike ikehu photon:
\[ E = \frac{hc}{\lambda} \]
E hoʻokomo i nā waiwai o ke kūpaʻa Planck (\( h = 6.626 \times 10^{-34} \) Js) a me ka wikiwiki o ka mālamalama \( c = 3 \times 10^8 \ \text{m/s} \):
\[ E = \frac{(6.626 \times 10^{-34} \ \text{Js}) \times (3 \times 10^8 \ \text{m/s})}{500 \times 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{500 \times 10^{-9}} \]
\[ E = 3.976 \times 10^{-19} \ \text{J} \]
No laila, ʻo ka ikehu o ka photon he \( 3.976 \times 10^{-19} \) joules.
Nīnau 2: Ke helu ʻana i ka alapine (frequency) o ka ikehu photon
Nīnau: Inā he ikehu ko ka photon he \( 2.5 \times 10^{-19} \) joules, he aha ke alapine (frequency) o ke kukui o ia photon?
Kūkākūkā:
Hoʻohana mākou i ka hoohalike kumu o ka ikehu photon:
\[ E = hf \]
Hoʻokaʻawale mākou i ke alapine (frequency) \( f \):
\[ f = \frac{E}{h} \]
E hoʻokomo i nā waiwai o ka ikehu \( E \) a me ke kūpaʻa Planck \( h \):
\[ f = \frac{2.5 \times 10^{-19} \ \text{J}}{6.626 \times 10^{-34} \ \text{Js}} \]
\[ f = 3.77 \times 10^{14} \ \text{Hz} \]
No laila, ʻo ke alapine (frequency) o ke kukui he \( 3.77 \times 10^{14} \ \text{Hz} \).
Nīnau 3: Hopena Photoelectric
Nīnau: Ma kahi hoʻokolohua hopena photoelectric, kuʻi kahi photon me ka ikehu 4.0 eV i kahi ʻili metala a hoʻokuʻu i kahi electron. Inā ʻo ka hana hana o ka metala he 2.5 eV, e helu i ka ikehu kinetic kiʻekiʻe loa o ka electron i hoʻokuʻu ʻia.
Kūkākūkā:
Hāʻawi ʻia ka ikehu photon \(E \) ma electronvolts (eV). Hiki iā mākou ke hoʻohana pololei i kēia waiwai no ka mea aia pū ka hana hana ma eV.
ʻO ka hana hana (\( W \)) ka ikehu liʻiliʻi loa e pono ai e wehe i kahi electron mai ka ʻili metala. Ua helu ʻia ka ikehu kinetic kiʻekiʻe loa (\( KE \)) o kahi electron ma ke ʻano he ʻokoʻa ma waena o ka ikehu photon a me ka hana hana:
\[ KE = E – W \]
E hoʻokomo i nā waiwai o ka ikehu photon \( E = 4.0 \ \text{eV} \) a me ka hana hana \( W = 2.5 \ \text{eV} \):
\[ KE = 4.0 \ \text{eV} – 2.5 \ \text{eV} \]
\[ KE = 1.5 \ \text{eV} \]
No laila, ʻo ka ikehu kinetic kiʻekiʻe loa o ka electron i hoʻokuʻu ʻia he 1.5 eV.
Nīnau 4: Ka lōʻihi o ka nalu mai ka alapine (frequency)
Nīnau: He aha ka nalu o kahi photon nona ka alapine (frequency) o \( 6 \times 10^{14} \ \text{Hz} \)?
Kūkākūkā:
Ke hoʻohana nei i ka pilina ma waena o ka wikiwiki o ka mālamalama, ke alapine (frequency), a me ka nalu lōʻihi:
\[ c = \lambda f \]
Hoʻokaʻawale mākou i ka nalu \( \lambda \):
\[ \lambda = \frac{c}{f} \]
E hoʻokomo i nā waiwai no ka wikiwiki o ka mālamalama \( c = 3 \times 10^8 \ \text{m/s} \) a me ke alapine (frequency \( f = 6 \times 10^{14} \ \text{Hz} \):
\[ \lambda = \frac{3 \times 10^8 \ \text{m/s}}{6 \times 10^{14} \ \text{Hz}} \]
\[ \lambda = 5 \times 10^{-7} \ \text{m} \]
\[ \lambda = 500 \ \text{nm} \]
No laila, ʻo ka nalu o ka photon he 500 nm.
Nīnau 5: Ikehu Photon i loko o ka Spectrum
Nīnau: He 150 nm ka lōʻihi o ka nalu o kahi photon i loko o ka spectrum ultraviolet. E helu i ka ikehu o ka photon ma joules a me electronvolts.
Kūkākūkā:
ʻO ka mea mua, e hoʻololi i ka nalu i nā mika:
\[ 150 \ \text{nm} = 150 \times 10^{-9} \ \text{m} \]
Ke helu nei i ka ikehu photon ma joules:
\[ E = \frac{hc}{\lambda} \]
E hoʻokomo i nā waiwai:
\[ E = \frac{(6.626 \times 10^{-34} \ \text{Js}) \times (3 \times 10^8 \ \text{m/s})}{150 \times 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{150 \times 10^{-9}} \]
\[ E = 1.3252 \times 10^{-18} \ \text{J} \]
No ka hoʻololi ʻana i nā joules i nā electronvolts, hoʻohana mākou i ka 1eV = \( 1.602 \times 10^{-19} \) J:
\[ E \ (\text{eV}) = \frac{1.3252 \times 10^{-18} \ \text{J}}{1.602 \times 10^{-19} \ \text{J/eV}} \]
\[ E \ (\text{eV}) = 8.27 \ \text{eV} \]
No laila, ʻo ka ikehu o ka photon ultraviolet he \( 1.3252 \times 10^{-18} \ \text{J} \) a i ʻole 8.27 eV.
Ka hopena
Mai nā pilikia hoʻohālike like ʻole a me nā kūkākūkā ma luna, ua ʻeli hohonu mākou i nā ʻano a me nā helu e pili ana i nā photons. Hoʻokomo pū kēia i ka helu ʻana i ka ikehu e pili ana i ka nalu a me ke alapine (frequency), a me ka hoʻopili ʻana o ka manaʻo photon i ka hopena photoelectric. He mea nui ka hoʻomaopopo ʻana i ka manaʻo photon ʻaʻole wale ma ka physics theoretical akā i nā noi ʻenehana hou like ʻole e like me nā photovoltaics, lasers, a me nā sensors kukui. Me ka lawa ʻana o ka hoʻomaʻamaʻa, e maʻalahi a ʻoi aku ka maʻalahi o ka hoʻomaopopo ʻana i kēia mau manaʻo.
