The successive ionization energies for a given element are listed. How many valence electrons does it have?

3 valence electrons

Explanation:

Let us first find the amount increased for everything.

From 1st to 2nd,  1048 - 620 = 428

428 increased from 1st to 2nd.

From 2nd to 3d, 2144 - 1048 = 1096

1096 increased from 2nd to 3rd.

From 3rd to 4th, 8724 - 2144 = 6580

6580 increased from 3rd to 4th.

From 4th  to 5th, 10141 - 8724 = 1417

From 3rd to 4th,  it increased the most. Therefore, we assume that those are the beginning core electrons and not valence electrons. Also, starting from 3rd, they are all core electrons.

For the 1st and 2nd,  we can assume they are valence electrons because the kJ/mol didn't increase that much.

Since the core electrons started from the 3rd, we most likely have 3 valence electrons.

So the final answer is 3.

Hope it helped!