Nā nīnau hoʻohālike e kūkākūkā ana i ka ikehu nalu electromagnetic
He kuleana koʻikoʻi ko ka ikehu nalu electromagnetic i nā ʻano hana ʻenehana a me nā noi ʻepekema like ʻole. Mai nā kamaʻilio lekiō a hiki i nā kukuna X-lapaʻau, he mea nui ka hoʻomaopopo ʻana i nā nalu electromagnetic a me ko lākou ikehu. E uhi kēia ʻatikala i nā manaʻo koʻikoʻi a hāʻawi i nā pilikia laʻana ma ka ikehu nalu electromagnetic, e uhi ana i nā ʻano kumumanaʻo a me nā ʻano hana.
Hoʻolauna i nā Nalu Uila
ʻO nā nalu electromagnetic he mau nalu i haku ʻia me nā kahua uila a me nā kahua magnetic oscillating, e hele ana ma ka lewa ma ka wikiwiki o ka mālamalama. Hoʻopuka ʻia lākou ma o ka hoʻololi ʻana o nā kahua uila a me nā kahua magnetic a hiki ke hoʻolaha ma o ka vacuum a i ʻole ma o nā mea media. Hoʻopuni ka spectrum electromagnetic i nā ʻano nalu like ʻole, mai nā nalu lekiō me nā nalu lōʻihi a hiki i nā kukuna gamma me nā nalu pōkole loa.
Ma keʻano laulā, hiki ke hōʻike ʻia ka ikehu o nā nalu electromagnetic ma ke ʻano o kahi hoohalike:
\[ E = h \cdot f \]
Ma hea ʻo \( E \) ka ikehu photon, ʻo \( h \) ke kūpaʻa o Planck (\(6.626 \times 10^{-34} \, \text{Js} \)), a ʻo \( f \) ke alapine nalu. Ke ʻike nei i ke alapine a i ʻole ka nalu (\( \lambda \)), hiki iā mākou ke helu i ka ikehu o ka nalu electromagnetic me ka hoʻohana ʻana i ka wikiwiki o ka mālamalama (\( c = 3 \times 10^8 \, \text{m/s} \)), ma hea \( c = \lambda \cdot f \).
Laʻana Nīnau 1
Nīnau:
He alapine (frequency) ko kahi nalu electromagnetic o \( 5 \times 10^{14} \, \text{Hz} \). E helu i ka ikehu o hoʻokahi photon o kēia nalu electromagnetic.
Kūkākūkā:
E hoʻohana i ka hoohalike \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ f = 5 \times 10^{14} \, \text{Hz} \]
No laila,
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (5 \times 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \times 10^{-19} \, \text{J} \]
ʻO ka ikehu o hoʻokahi photon o ka nalu electromagnetic ʻo \( 3.313 \times 10^{-19} \, \text{J} \).
Laʻana Nīnau 2
Nīnau:
Inā he nalu ko ka radiation \( \lambda \) o \( 600 \, \text{nm} \), e helu i kona ikehu no kēlā me kēia photon ma nā electron volts (eV). (Hāʻawi ʻia: 1 eV = \( 1.602 \times 10^{-19} \, \text{J} \)).
Kūkākūkā:
ʻO ka mea mua, e hoʻololi i ka nalu i hāʻawi ʻia i mau mika:
\[ \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \]
E hoʻohana i ka pilina \( c = \lambda \cdot f \) e ʻike i ke alapine (frequency):
\[ c = 3 \times 10^8 \, \text{m/s} \]
\[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{600 \times 10^{-9} \, \text{m}} \]
\[ f = 5 \times 10^{14} \, \text{Hz} \]
I kēia manawa, e helu i ka ikehu photon me ka hoʻohana ʻana i \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (5 \times 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \times 10^{-19} \, \text{J} \]
I kēia manawa, e hoʻololi i ka ikehu i nā electron volts:
\[ E = \frac{3.313 \times 10^{-19} \, \text{J}}{1.602 \times 10^{-19} \, \text{J/eV}} \]
\[ E \approx 2.07 \, \text{eV} \]
No laila, ʻo ka ikehu no kēlā me kēia photon o ka radiation me ka nalu lōʻihi \( 600 \, \text{nm} \) ma kahi o 2.07 eV.
Laʻana Nīnau 3
Nīnau:
ʻO ka nalu o nā microwave he \( 12 \, \text{cm} \). E hoʻoholo i ka ikehu o hoʻokahi photon o kēia microwave.
Kūkākūkā:
ʻO ka mea mua, e hoʻololi i ka nalu i hāʻawi ʻia i mau mika:
\[ \lambda = 12 \, \text{cm} = 12 \times 10^{-2} \, \text{m} \]
E hoʻohana i ka pilina \( c = \lambda \cdot f \) e ʻike i ke alapine (frequency):
\[ c = 3 \times 10^8 \, \text{m/s} \]
\[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{12 \times 10^{-2} \, \text{m}} \]
\[ f = 2.5 \times 10^9 \, \text{Hz} \]
I kēia manawa, e helu i ka ikehu photon me ka hoʻohana ʻana i \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (2.5 \times 10^9 \, \text{Hz}) \]
\[ E = 1.6565 \times 10^{-24} \, \text{J} \]
ʻO ka ikehu o hoʻokahi photon o nā microwaves me ka nalu lōʻihi \( 12 \, \text{cm} \) ʻo \( 1.6565 \times 10^{-24} \, \text{J} \).
Laʻana Nīnau 4
Nīnau:
E helu i ka helu o nā photons i hana ʻia e kahi laser me ka mana \( 1 \, \text{W} \) e hoʻopuka ana i ka mālamalama me ka nalu \( 500 \, \text{nm} \) no \( 1 \, \text{s} \).
Kūkākūkā:
ʻO ka mea mua, e helu i ka ikehu o kahi photon hoʻokahi me ka nalu \( 500 \, \text{nm} \):
\[ \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \]
E hoʻohana i ka pilina \( c = \lambda \cdot f \) e ʻike i ke alapine (frequency):
\[ c = 3 \times 10^8 \, \text{m/s} \]
\[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{500 \times 10^{-9} \, \text{m}} \]
\[ f = 6 \times 10^{14} \, \text{Hz} \]
Ke hoʻohana nei iā \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (6 \times 10^{14} \, \text{Hz}) \]
\[ E = 3.9756 \times 10^{-19} \, \text{J} \]
I kēia manawa, e helu i ka helu o nā photons i hoʻokuʻu ʻia i ka wā o \( 1 \, \text{s} \):
Mana \( P = 1 \, \text{W} \):
\[ E_{\text{total}} = P \cdot t = 1 \, \text{W} \times 1 \, \text{s} = 1 \, \text{J} \]
Helu o nā photons:
\[ n = \frac{E_{\text{total}}}{E_{\text{photons}}} = \frac{1 \, \text{J}}{3.9756 \times 10^{-19} \, \text{J}} \]
\[ n \approx 2.52 \times 10^{18} \]
No laila, hoʻopuka ka laser ma kahi o \( 2.52 \times 10^{18} \) photons i hoʻokahi kekona.
Ka hopena
ʻO ka hoʻomaopopo ʻana i ka ikehu nalu electromagnetic ke kī i nā noi he nui ma nā ʻano like ʻole o ka ʻenekinia a me ka ʻepekema. Ma o nā laʻana i kūkākūkā ʻia, ua ʻike mākou i nā ʻanuʻu e pili ana i ka helu ʻana i ka ikehu photon e pili ana i ka alapine (frequency) a me ka nalu (wavelength), ka hoʻololi ʻana ma waena o nā ʻāpana ikehu, a me ka helu ʻana i ka mana radiant. Me ka hoʻomaʻamaʻa a me ka hoʻomaopopo hohonu, e lilo kēia mau manaʻo i mea maʻalahi a pono i nā noi o ke ao maoli.
