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First of all this is not Carbon's valency, it is electronic configuration or arrangement of electrons around nucleus.

Electron filling takes place by Aufbau principle.

Explanation: Electrons around an atom are arranged in shells( denoted by n) numbered 1, 2, 3, and so on. Each of these shells is further divided into s,p,d,f subshells(denoted by l).

It is known that electrons in a subshell have same energy. Electron filling occurs 1st in subshells of lower energy and higher energy subshell is filled only after the lower subshell is completely filled (Aufbau principle). Subshell whose n+l sum is less has lower energy. So here 2s(n+l=2) shell is lower to 2p(n+l=3), and 2s can have 2 electrons so after 2s is filled 2 electrons left go to 2p subshell.

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Q: Actually carbon valency written as 1s2 2s2 2p2.why not this is write as 1s2 2s1 2p3?
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