Basic Modern Physics
13.0 Atomic Excitation
13.0 Atomic Excitation
It can be be carried out by two of the following methods:
1. By photon absorption
2. By collision
Let us discuss each of these in details.
1. Photon absorption:
An electron gets excited to higher state on absorption of photon. This is also known as spontaneous absorption. Only those photons are absorbed which have an energy equal to the energy difference of ground state and any excited state. The electrons are thus, excited to subsequent excited state. However, as each state has its own decay time and the number of electron in the inner orbit must be $2{n^2}$, the electron excited returns to ground state with emission of photon of energy equal to the energy difference between the two states.
Example. For an electron to be excited to $n=2$ from $n=1$ in ${\text{H}}{{\text{e}}^ + }$ a photon of energy equal to (-13.6-(-54.4))= 40.8 $eV$ is required (and necessary).
This also is the primary reason behind the origin of spectra, namely absorption and emission spectrum.
Emission Spectrum:
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state.
When a solid is heated, its atoms collide with each other and as a result orbital electrons are excited to higher states. Radiation of wavelength corresponding to energy equal to the energy difference between the two states is released on de-excitation. Generally, the radiation emitted consists of a bunch of wavelength. When the radiations are observed in order of their wavelengths we get a spectrum known as emission spectrum.
Absorption Spectrum:
Absorption spectrum is the characteristic pattern of dark lines or bands that occurs when electromagnetic radiation from a light source emitting full spectrum is passed through an absorbing medium into a spectroscope. An equivalent pattern occurs as colored lines or bands in the emission spectrum of that medium.
Clearly, absorption spectrum and emission spectrum are complimentary to each other.
The study of absorption spectra led Kirchoff to formulae the following law, known as Kirchoff's Law:
"If a substance emits of a certain wavelength at a given temperature, then it will absorb the same wavelength selectively, when light passed through the substance in vapor state. It follows from the fact that emission and absorption spectra are complimentary."
2. Atomic collision:
For atomic excitation to occur by atomic collision, must be inelastic in nature and the kinetic energy lost in this process is used for atomic excitation. Numerical problems can be worked out by using the following principles:
- Conservation of linear momentum (CLM)
- Conservation of energy (CE)
Example. Consider a head-on-collision of a moving neutron (mass= $m$, velocity= $u$) and stationary $H{e^ + }$(mass= $2m$).
For perfectly elastic collision: There will no energy loss implying no excitation of $He$ atom due to collision.
For perfectly inelastic collision: Let their common speed after collision be $v$. By CLM,
$$\begin{equation} \begin{aligned} mu = 3mv \\ {\text{or }}v = \frac{u}{3}...(i) \\\end{aligned} \end{equation} $$
Loss of energy,
$$\begin{equation} \begin{aligned} \Delta E = {E_i} - {E_f} \\ {\text{ }} = \frac{1}{2}m{u^2} - \frac{1}{2}\left( {3m} \right){v^2} \\ {\text{ }} = \frac{1}{2}m{u^2} - \frac{1}{2}\left( {3m} \right){\left( {\frac{u}{3}} \right)^2} \\ {\text{ }} = \frac{1}{3}m{u^2} \\ {\text{ }} = \frac{{{E_i}}}{3} \\\end{aligned} \end{equation} $$
This loss in energy is absorbed by helium only when this energy is equal to the minimum energy required to excite the $H{e^ + }$ (=40.8 $eV$) which is when it excites from $n= 1$ to $n= 2$. If the loss in perfectly inelastic collision $ > 40.8\ eV$ then $H{e^ + }$ may absorb 40.8 $eV$ for its excitation and rest of the energy will remain in the colliding particles as their kinetic energies and the collision will not be perfectly inelastic.
So, it is better to assume perfectly inelastic collision to find out maximum energy loss that can happen and then test whether the collision is perfectly inelastic or inelastic in nature depending upon the energy consumption for excitation.
