The metallic lustre of potassium is explained by:
Diffusion of ions
Oscillation of mobile free electrons
Existence of body centred cubic lattice
Existence of free protons
As we have learned
Metallic Lustre -
It is due to delocalised mobile electrons.The loosely bound electron absorbs energy from light and starts vibrating at a frequency equal to that of incident light.The vibrating electron emits EM wave and it gives shining appearance known as metallic lustre.
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When light falls on potassium, the free electrons starts oscillating at their mean position and gets excited to higher energy level. These electrons come back to the ground state by emitting light which spread in all directions.
Therefore, Option(2) is correct.