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Found in: Page 279

### Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

# (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 ${{\mathbit{m}}}_{{\mathbf{l}}}$?

1. For a one dimensional particle in a box, the n represents the shell to which electron belongs. The value of n may be $1,2,3,.............n$.
2. In hydrogen, 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
3. Angular quantum number, l : represents the shape of the orbital of hydrogen Magnetic quantum number, ${m}_{l}$: represents the energy levels in sub shell.
See the step by step solution

## Step 1: Quantum numbers

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 (${{m}}_{{l}}$) and spin quantum number (${{m}}_{{s}}$).

## Step 2: (a) The significance of n for 1D particle in a box

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 $1,2,3,.............n$

## Step 3: (b) To determine the meaning of  for a hydrogen atom

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.

## Step 4: (c) To determine the meaning andfor hydrogen atom

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, ${m}_{l}$.

Hence, Angular quantum number, l : represents the shape of the orbital of hydrogen Magnetic quantum number,${m}_{l}$ : represents the energy levels in sub shell.