when a gas like hydrogen is heated it shows discrete line in its emission spectrum but in case of solids we see a continuous spectrum why it is so???i have searched it on internet and some people says that solids also shows line spectrum but the difference in energy levels of electrons in solids is very less so it shows very dense line which our eyes cannot detect? if is it true then how black body absorbs all the frequency of radiation and emits also it should emits energy only of discrete frequencies?
Asked
Active
Viewed 224 times
1 Answers
4
This has to do with the energy eigenstates available to electrons inside a hydrogen atom versus a solid, say, electrons moving around inside a crystal ion lattice. You can also think of it as being about the number of separate degrees of freedom.
The intuitive picture is that a hydrogen atom is like (though not identical to) a harmonic oscillator with very high characteristic frequency $ \omega $ (or, equivalently, very small characteristic wavelength). The result of this is that the energy eigenstates form discrete "lines" spaced apart by large jumps on the order $ O(\hbar \omega) $. In terms of the actual diameter $ d $ of the atom, you can say the gap between the first energy levels is about $ O(\hbar^2 /(m_e d^2)) $ where $ m_e $ is the electron mass. (I emphasize that this is a very rough approximation.)
Now imagine a very large crystal lattice with very weak potential. What turns out to happen is that the energy eigenstates of such a lattice are spaced $ O(\hbar^2/(m_e L^2)) $ apart where $ L $ is the length of the entire piece of solid, which is orders of magnitude bigger than the size of a single atom. Consequently, in practice you can treat these energy states as practically continuous bands. However, when you take into account a weak periodic potential, "band gaps" open up between these continuous bands which are of considerable size relative to the negligible gaps between eigenstates in a single band, and it's this band gap structure that defines the absorption or emission of photons by a crystal lattice with weak periodic potential. (What I described is known as the nearly free electron model.)
A black body is a hypothetical entity which absorbs completely incident radiation at all frequencies. It is an idealized construction and doesn't refer to some object in the world. Nevertheless, if you have some body with negligible gaps between its technically discrete energy levels that looks "black", what is happening is that almost all of the energy in the incident light is going into some vibrational or rotational degrees of freedom inside the lattice, and perhaps a trace amount of it escapes in the form of infrared re-radiation. For practical purposes, you can consider such a body as being a perfect absorber of light in that specific frequency range.
Ege Erdil
- 561