91影视

The energy between any two adjacent vibrational levels is given by

$鈭�E=\frac{h}{2\mathrm{蟺}}蝇$

Where,$蝇$ is oscillating angular frequency and is spring constant .

Planck鈥檚 quantum theory

1.Diffrent atoms and molecules can emit or absorb energy in discrete quantities known as quantum.

2. The energy of the radiation absorbed or emitted is directly proportional to the frequency of radiation.

Mathematically energy of radiation is given by

$$\begin{gathered} E=hv \\ E=\frac{hc}{位} \end{gathered}$$

Where, E is the energy of the radiation, h is the Planck鈥檚 constant ,$位$ is the wavelength of emitted light and c is the speed of light.

Using

$$\begin{gathered} E=\frac{hc}{位} \\ E=\frac{6.63脳{10}^{鈭�34}\mathrm{J}.\mathrm{s}脳3.0脳{10}^8\mathrm{m}/\mathrm{s}}{2.39脳{10}^{鈭�6}\mathrm{m}} \\ E=8.32脳{10}^{鈭�20}\mathrm{J} \end{gathered}$$

Here, the energy emitted by photon equals the energy difference between two adjacent vibrational states

So,

$$\begin{gathered} 螖E=E \\ 螖E=8.32脳{10}^{-20}J \end{gathered}$$

Using

$\begin{array}{r}\mathrm{螖}E=\frac{h}{2蟺}蝇\\ 蝇=\frac{2蟺\mathrm{螖}E}{h}\end{array}$

Put the values of constants in above equation

$$\begin{gathered} 蝇=\frac{2蟺\mathrm{螖}E}{h} \\ 蝇=2蟺脳\frac{8.32脳{10}^{鈭�20}\mathrm{J}}{6.63脳{10}^{鈭�34}\mathrm{J}.\mathrm{s}} \\ 蝇=2蟺脳1.26脳{10}^{14}\mathrm{rad}/\mathrm{s} \end{gathered}$$

Using

$f=\frac{蝇}{2\mathrm{蟺}}$

Now put the values of constants in above relation

$\begin{array}{r}f=\frac{2蟺脳1.26脳{10}^{14}}{2蟺}\\ f=1.26脳{10}^{14}\mathrm{Hz}\end{array}$

Thus, the molecule of two masses of oxygen and hydrogen is making $1.26脳{10}^{14}$cycles per second