in thermal equilibrium at t=300k the ratio of level population n2/n1 for particular pair of level is given 1/e calculate frequency for this transition in what region of the EM spectrum does this frequency fall.
Answers
Answer:
Explanation:
o understand the concept of a population inversion, it is necessary to understand some thermodynamics and the way that light interacts with matter. To do so, it is useful to consider a very simple assembly of atoms forming a laser medium.
Assume there is a group of N atoms, each of which is capable of being in one of two energy states: either
The ground state, with energy E1; or
The excited state, with energy E2, with E2 > E1.
The number of these atoms which are in the ground state is given by N1, and the number in the excited state N2. Since there are N atoms in total,
where T is the thermodynamic temperature of the group of atoms, and k is Boltzmann's constant.
We may calculate the ratio of the populations of the two states at room temperature (T ≈ 300 K) for an energy difference ΔE that corresponds to light of a frequency corresponding to visible light (ν ≈ 5×1014 Hz). In this case ΔE = E2 - E1 ≈ 2.07 eV, and kT ≈ 0.026 eV. Since E2 - E1 ≫ kT, it follows that the argument of the exponential in the equation above is a large negative number, and as such N2/N1 is vanishingly small; i.e., there are almost no atoms in the excited state. When in thermal equilibrium, then, it is seen that the lower energy state is more populated than the higher energy state, and this is the normal state of the system. As T increases, the number of electrons in the high-energy state (N2) increases, but N2 never exceeds N1 for a system at thermal equilibrium; rather, at infinite temperature, the populations N2 and N1 become equal. In other words, a population inversion (N2/N1 > 1) can never exist for a system at thermal equilibrium. To achieve population inversion therefore requires pushing the system into a non-equilibrated state.