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$
\sigma T^4=\langle F_{\rm abs}\rangle=\frac{(1-A)\,I_a}{4}.
$
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$c = f\lambda\quad\Rightarrow\quad \lambda=\frac{c}{f}$
$
\lambda=\frac{3.0\times10^8\;\mathrm{m\,s^{-1}}}{6.48\times10^{13}\;\mathrm{Hz}} =4.63\times10^{-6}\;\mathrm{m}
$
$
\boxed{\lambda = 4.63\;\mu\text{m}}
$
The infrared radiation at that wavelength is absorbed by water vapour because it matches one of its vibrational frequencies.
> The frequency of the radiation probably matches that of one of the asymmetric vibrational modes of water molecules. In such a case, water molecules would absorb radiation of this frequency resulting in a low percent transmittance.
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assumptions of idea gas
![[Screenshot 20251007 at
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**Oscillation:** SA **repeated back-and-forth motion** of an object about its equilibrium (or mean) position.
**Simple harmonic oscillation (SHM):** An oscillation in which the **acceleration of the object is directly proportional to its displacement from the equilibrium position** and **acts in the opposite direction** to the displacement.
$a \propto -x \quad \text{or} \quad a = -\omega^2 x$
Transverse wave -- a wave in which the direction of energy propagation is at right angles to the direction of vibration of the particles of the medium through which the wave is travelling