91影视

The given data can be listed below as,

• The energy in the third excited state is, $E_3=-1.0\text{eV}$
• The energy in the second excited state is, $E_2=-1.8\text{eV}$
• The energy in the first excited state is, $E_1=-2.9\text{eV}$
• The energy in the ground state is,

The change in the photon energies is equal to the difference between the energy in the higher state and the energy in the ground state.

The equation of the photon energies can be expressed as,

$螖E=E_f-E_0$ 鈥�(1)

Here,$螖E$ is the emitted energy of photon, $E_f$ is the energy in excited state and $E_0$ is energy in the ground state.

(a)

For the electrons going from the ground state to the first excited state,

For $E_f=E_1=-2.9\text{eV}$and $E_0=-4.8\text{eV}$in equation (1).

$$\begin{gathered} 鈻�E=-2.9eV-(-4.8eV) \\ =1.9eV \end{gathered}$$

For the electrons going from the ground state to the second excited state,

For $E_f=E_2=-1.8\text{eV}$and $E_0=-4.8\text{eV}$in equation (1).

$$\begin{gathered} 鈻�E=-1.8eV-(-4.8eV) \\ =3eV \end{gathered}$$

For the electrons going from the ground state to the third excited state,

For $E_f=E_3=-1.0\text{eV}$and $E_0=-4.8\text{eV}$in equation (1).

$$\begin{gathered} 鈻�E=-1.0eV-(-4.8eV) \\ =3.8eV \end{gathered}$$

For the electrons going from the first excited state to the second excited state, the equation becomes,

$螖E=E_f-E_1$ 鈥�(2)

Here, $螖E$is the energy emitted by the photon, $E_f$is the energy of the other excited state and $E_1$is the energy of the first excited state

For the electrons going from the first excited state to the second excited state

For $E_f=E_2=-1.8\text{eV}$and $E_1=-2.9\text{eV}$in equation (2).

$$\begin{gathered} 鈻�E=-1.8eV-(-2.9eV) \\ =1.1eV \end{gathered}$$

For the electrons going from the first excited state to the third excited state.

For $E_f=E_3=-1.0\text{eV}$and$E_1=-2.9\text{eV}$in equation (2).

$$\begin{gathered} 鈻�E=-1.0eV-(-2.9eV) \\ =1.9eV \end{gathered}$$

For the electrons going from the second excited state to the third excited state, the equation becomes,

$螖E=E_f-E_2$ 鈥�(3)

Here, $螖E$is the energy emitted by the photon, $E_f$is the energy of the other excited state and $E_2$is the energy of the second excited state.

For $E_f=E_3=-1.0\text{eV}$and$E_2=-1.8\text{eV}$in equation (3).

$$\begin{gathered} 鈻�E=-1.0eV-(-1.8eV) \\ =0.8eV \end{gathered}$$

Thus, the six energies of photon that could be strongly emitted by the material or the list of the photon emission energies are $1.9\text{eV}$, $3\text{eV}$, $3.8\text{eV}$, $1.1\text{eV}$, $1.9\text{eV}$and $0.8\text{eV}$.

(b)

The dark lines in the spectrum indicates that no electrons are available in the exited state due to the possible transitions of the electrons. However, when a large amount of energy strikes, the energy frequencies are absorbed as the black bands inside the spectrum. Hence, the missing dark lines are the transition of the energy between the ground state to the first, second and the third excited state which are $1.9\text{eV}$, $3\text{eV}$, $3.8\text{eV}$respectively.

Thus, the missing lines or the dark-line energies in the spectrum are $1.9\text{eV}$, $3\text{eV}$, $3.8\text{eV}$.