Even though most certifying agencies still require the use of the snorkel, the fact of the matter is they are unneeded, cumbersome, and are rarely used. The main purpose for them in scuba, as is stated in the textbooks, is to allow the diver to swim on the surface for long distances without the need for trying to breathe by lifting the head out of the water. If the thumb fits snugly in the top of the snorkel it is correct. A snorkel bore that is too small will not allow enough air to flow through and will make breathing hard. One that is too large will be difficult to clear water from.
Some snorkels have a flexible section near the mouthpiece.
The section is corrugated so if it is bent it will not close. The reason for the flex is to allow the snorkel to hang straight when not in use. In that way it does not interfere with the scuba regulator. Be sure the interior of the corrugated section is smooth. The corrugations should not continue on the inside because water will trickle down the grooves and into the diver's mouth.