91影视

The expression for the energy of the oscillator is given by,

${\mathbf{E}}_{\mathbf{N}}\mathbf{=}{\mathbf{狈丑蝇}}_{\mathbf{0}}\mathbf{+}{\mathbf{E}}_{\mathbf{0}}$

Here $\mathrm{N}=0,1,2,\text{鈥�}\mathrm{....}$

The angular frequency is given by,

${\mathrm{蝇}}_0=\sqrt{\frac{{\mathrm{k}}_{\mathrm{s}}}{\mathrm{m}}}$

Here${\mathrm{蝇}}_0$ is the angular frequency,${\mathrm{k}}_{\mathrm{s}}$ is the spring constant,$\mathrm{m}$ is the mass.

The ground state energy of the harmonic oscillator is given by,

${\mathrm{E}}_0=\frac{1}{2}{\mathrm{h蝇}}_0$

The spacing between the energy level is given by,

$\mathrm{螖贰}=0.4\text{鈥�}\mathrm{eV}$

${\mathrm{h蝇}}_0=0.4\text{鈥�}\mathrm{eV}$

The expression for energy of the photon which is emitted during the transition from $3鈫�2$is given by,

$\begin{array}{c}{\mathrm{E}}_3鈭�{\mathrm{E}}_2=(3{\mathrm{h蝇}}_0+{\mathrm{E}}_0)鈭�(2{\mathrm{h蝇}}_0+{\mathrm{E}}_0)\\ ={\mathrm{h蝇}}_0\end{array}$

Substitute$0.4\text{鈥�}\mathrm{eV}$ for ${\mathrm{h蝇}}_0$into the above equation,

${\mathrm{E}}_3鈭�{\mathrm{E}}_2=0.4\text{鈥�}\mathrm{eV}$

The expression for energy of the photon which is emitted during the transition from$3鈫�0$is given by,

$\begin{array}{c}{\mathrm{E}}_3鈭�{\mathrm{E}}_0=(3{\mathrm{h蝇}}_0+{\mathrm{E}}_0)鈭�\left({\mathrm{E}}_0\right)\\ =3{\mathrm{h蝇}}_0\end{array}$

Substitute$0.4\text{鈥�}\mathrm{eV}$ for ${\mathrm{h蝇}}_0$into the above equation,

$\begin{array}{c}{\mathrm{E}}_3鈭�{\mathrm{E}}_0=3\left(0.4\text{鈥�}\mathrm{eV}\right)\\ =1.2\text{鈥�}\mathrm{eV}\end{array}$

The expression for energy of the photon which is emitted during the transition from$2鈫�0$is given by,

$\begin{array}{c}{\mathrm{E}}_2鈭�{\mathrm{E}}_0=(2{\mathrm{h蝇}}_0+{\mathrm{E}}_0)鈭�\left({\mathrm{E}}_0\right)\\ =2{\mathrm{h蝇}}_0\end{array}$

Substitute$0.4\text{鈥�}\mathrm{eV}$for ${\mathrm{h蝇}}_0$into the above equation,

$\begin{array}{c}{\mathrm{E}}_3鈭�{\mathrm{E}}_0=2\left(0.4\text{鈥�}\mathrm{eV}\right)\\ =0.8\text{鈥�}\mathrm{eV}\end{array}$

The expression for energy of the photon which is emitted during the transition from$3鈫�1$is given by,

$\begin{array}{c}{\mathrm{E}}_3鈭�{\mathrm{E}}_1=(3{\mathrm{h蝇}}_0+{\mathrm{E}}_0)鈭�({\mathrm{h蝇}}_0+{\mathrm{E}}_0)\\ =2{\mathrm{h蝇}}_0\end{array}$

Substitute $0.4\text{鈥�}\mathrm{eV}$ for ${\mathrm{h蝇}}_0$into the above equation,

$\begin{array}{c}{\mathrm{E}}_3鈭�{\mathrm{E}}_0=2\left(0.4\text{鈥�}\mathrm{eV}\right)\\ =0.8\text{鈥�}\mathrm{eV}\end{array}$

The expression for energy of the photon which is emitted during the transition from$1鈫�0$is given by,

$\begin{array}{c}{\mathrm{E}}_1鈭�{\mathrm{E}}_0=({\mathrm{h蝇}}_0+{\mathrm{E}}_0)鈭�\left({\mathrm{E}}_0\right)\\ ={\mathrm{h蝇}}_0\end{array}$

Substitute$0.4\text{鈥�}\mathrm{eV}$ for ${\mathrm{h蝇}}_0$into the above equation,

${\mathrm{E}}_3鈭�{\mathrm{E}}_0=0.4\text{鈥�}\mathrm{eV}$

Therefore, the photon energies for the given system are $0.4\text{鈥�}\mathrm{eV}$(three transitions),$0.4\text{鈥�}\mathrm{eV}$ (Two transitions), and $1.2\text{鈥�}\mathrm{eV}$(one transition).