What is the most valuable piece on the chess board after the queen?

Do you mean "valuable" or "powerful"?
Obviously, the king is the most valuable piece, since if you "lose" it, you lose the game - no arguments. But it's not the most powerful. It becomes an attacking piece only in the endgame.
In most positions, the queen is the most powerful, as she has the longest reach over more possible squares. The rook is generally considered to be the next most powerful, again because of its possible long reach along rank and file.
However, the knight and bishop can do things that the rook can't. So, as often, it all depends on the game position: "circumstances alter cases".

1.King(∞)
2.Queen(9)
3.Rooks(5)
4.Bishop(3.5) and Knight(3)
5.Pawns (1)

That all depends on the position at the time.
In the starting position the King is.

Depends on your playing style, I personally like using rooks

The King is the most valuable. Without, you have lost. Then the queen, which is worth 9 points. The rook is worth 5 points and is next in line as the most valuable piece.

Before queen king is valuble

king...