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5. Imagine that an aluminum nanoparticle has 8.4 x 106 atoms and has an energy band structure which is a fairly close approxi

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Answer #1

The atomic energy levels of a single atom is discrete. But when more than one atom is held together, the energy level gets split.

If there are 2 atoms, there will be two discrete energy levels, for each energy level that was present in the single atom.

For N atoms, there will be N energy levels.

Now, in the case of aluminium, the 2p orbital is completely filled.

In a 2p sub band, there are 3 discrete energy levels

2p_x,2p_y \;\&2p_z

So, if there are N atoms in the nano particle, this will split into 3N energy levels.

Here, N = 8.4*106 atoms.

So, no of discrete energy levels = 3*N = 3*8.4*106 = 2.52*107 energy levels.

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