Energy Bands in solids

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Joined Aug 19, 2011
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Considering isolated Lithium atom which has 3 electrons, K shell will have 2 electrons with energy -13.6eV. L shell will have 1 electron with energy -3.4eV. Now , considering a small piece of Lithium metal containing 100 atoms, then there would be 100 K levels and 100 L levels differing in energy by extremely small amounts. We call it as energy band.
Why there is small change in energy when there is energy band, while there is no energy change for isolated atoms?