91影视

The wavelength of the transition between the energy levels,$位=580\mathrm{nm}$

The temperature of the sample, T =300 K

The number of atoms in the lower state without external process, $N_1=4脳{10}^{20}\mathrm{atoms}$

The number of atoms in the upper state with external process or number of the emitting photons,$N_1=3脳{10}^{20}\mathrm{atoms}$

The number of atoms in the lower state without external process or the atoms absorbing photons,

$N_2=1脳{10}^{20}\mathrm{atoms}$

Consider the known data below.

The Plank鈥檚 constant is,

$$\begin{gathered} h=6.63脳{10}^{-34}J.s \\ =\left(6.242脳{10}^{18}脳6.63脳{10}^{-34}\right)eV.s \\ =41.384脳{10}^{-16}eV.s \end{gathered}$$

The speed of light is,

$$\begin{gathered} \mathrm{c}=3脳{10}^8\mathrm{m}/\mathrm{s} \\ =\left(3脳{10}^8脳{10}^9\right)\mathrm{nm}/\mathrm{s} \\ =3脳{10}^{17}\mathrm{nm}/\mathrm{s} \end{gathered}$$

The law states that the chances of a molecule gaining energy decreases with increasing energy equal to the Boltzmann factor $\mathbf{exp}\mathbf{(}\mathbf{-}\mathbf{蔚}\mathbf{/}\mathbf{kT}\mathbf{)}$.

Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the magnetic frequency of the photon and thus, equally, equates to the wavelength of the wave. When the frequency of photons is high, its potential is high.

Using the Boltzmann-distribution equation which is the expression for the probability for stimulated emission of radiation to the probability for spontaneous emission of radiation under thermal equilibrium, we can get the number of photons present in the upper energy level. Again, using the same relation with Planck's equation, the maximum energy can be calculated.

Formula:

The Boltzmann energy distribution equation,

$\frac{{\mathrm{N}}_1}{{\mathrm{N}}_2}={\mathrm{e}}^{-\left({\mathrm{E}}_2-{\mathrm{E}}_1\right)/\mathrm{kT}}$ 鈥�.. (1)

Here, the Boltzmann constant is,$\mathrm{k}=1.38脳{10}^{-23}\mathrm{J}/\mathrm{K}$

The energy of the photon due to Planck鈥檚 relation,

$\mathrm{E}=\frac{\mathrm{hc}}{\mathrm{位}}$ 鈥�.. (2)

Using the given data and equation (2) in equation (1) before any application of an external process, the value of the number of photons present in the upper energy level of the transition is as follows.

$$\begin{gathered} {\mathrm{N}}_1={\mathrm{N}}_2{\mathrm{e}}^{-\mathrm{hc}/\mathrm{位办罢}} \\ =\left(4脳{10}^{20}\right)\exp \left[\frac{\left(41.384脳{10}^{-16}\mathrm{eV}.\mathrm{s}\right)\left(3脳{10}^{17}\mathrm{nm}/\mathrm{s}\right)}{\left(580\mathrm{nm}\right)\left(8.62脳{10}^{-5}\mathrm{eV}/\mathrm{K}\right)\left(300\mathrm{K}\right)}\right] \\ =5脳{10}^{-16} \\ 1\left(\mathrm{Case}\mathrm{is}\mathrm{not}\mathrm{possible}\right) \end{gathered}$$

Hence, there are no electrons in the upper energy level.

With the application of the external process, the net output energy considering the number of photons and energy relation can be given energy of photon from equation (2) as follows.

$$\begin{gathered} \mathrm{E}=\left({\mathrm{N}}_1-{\mathrm{N}}_2\right)\frac{\mathrm{hc}}{\mathrm{位}} \\ =\left(3脳{10}^{20}-1脳{10}^{20}\right)\frac{\left(6.63脳{10}^{-34}\mathrm{J}.\mathrm{s}\right)\left(3脳{10}^8\mathrm{m}/\mathrm{s}\right)}{\left(580脳{10}^{-9}\mathrm{m}\right)} \\ =68\mathrm{J} \end{gathered}$$

Hence, the value of the maximum energy is 68 J.