how can the maximum number of electrons that can be accommodated in the outermost orbit is eight  ????

This is according to the octet rule, according to which in order to have maximum stability an atom must have 8 electrons in its valence shell.

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The maximum number of electrons that can be accommodated in a shell is given by the formula 2n2, where n denotes the shell number. Thus, since for the K shell, n = 1, hence the maximum number of electrons that can be accommodated in the K shell is 2 X (1)2 = 2. Similarly, the L shell can accommodate a maximum of 8 electrons, while the M and the N shell can accommodate a maximum of 18 and 32 electrons respectively. 

If, however, a given shell is the outermost shell, it cannot hold more than 8 electrons. For example, the M shell can hold a maximum of 18 electrons, but if it is the outermost shell, then it cannot hold more than 8 electrons. Similar is the case with the N shell. It has the capacity to hold maximum of 32 electrons. But if it is the outermost shell, then it cannot hold more than eight electrons.

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This can be calculated by the formula 2n2

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