(a) For one-dimensional particle in a box, what is the meaning of n? Specifically, what does knowing n tell us? (b) What is the meaning of n for a hydrogen atom? (c) For a hydrogen atom. What is the meaning of l and ?
Quantum numbers are the values which determine the position and energy of an electron in an atom, there are four types of quantum numbers, principal (n ) azimuthal (l ), magnetic () and spin quantum number ().
The Quantum-mechanical model of an atom provides us with a few quantum numbers which helps to determine the exact location of electron in an atom.
The first quantum number is the principal quantum number which is represented by n , it represents the shell number to which an electron belongs.
Hence, for a one dimensional particle in a box, the n represents the shell to which electron belongs. The value of n may be
In hydrogen atom, principal quantum number holds a great significance. It can specify the radial distributions of the wave function and the energy values of the atom with different n values.
It also specifies the radial dependence of the radial wave function.
Just like principal quantum number, there are three more quantum numbers, out of which two are - angular quantum number, l and the magnetic quantum number, .
Hence, Angular quantum number, l : represents the shape of the orbital of hydrogen Magnetic quantum number, : represents the energy levels in sub shell.
Classically, it was expected that an orbiting electron would emit radiation of the same frequency as its orbit frequency. We have often noted that classical behaviour is observed in the limit of large quantum numbers. Does it work in this case? (a) Show that the photon energy for the smallest possible energy jump at the “low-n-end” of the hydrogen energies is , while that for the smallest jump at the “high-n-end” is , where is hydrogen’s ground-state energy. (b) Use F=ma to show that the angular velocity of a classical point charge held in orbit about a fixed-point charge by the coulomb force is given by . (c) Given that , is this angular frequency equal to the minimum jump photon frequency at either end of hydrogen’s allowed energies?
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