100 milliamp coil current...transistor or MOSFET?

Why dose every one think that a Atmega 328p can source and sink 40 mA the datasheet said that's not going to happen the chips VCC and Gnd pins can only source and sink 200 mA now there 23 I/O on that chip do the math 23 times 40

That's almost a 1Amp Now you can sink or source 40 mA on 4 pins max if you go over that your over the max spec for that chip. One pin may even handle 80mA for a short time depending on how big the power bus is in the chip but I wouldn't use that chip for anything that you want to work day to day.

If you want to drive a 2n2222 or a 2n7000 use a resistor that limits the pin output to 10mA.

Why it's 40mA a pin if that was true the VCC would need more pins and so would the gnd and the max would not be

DC Current VCC and GND Pins................................ 200.0 mA

And the first time you drive 320mA out a port see how long you chip can handle that before it shuts down.

This is the Absolute Maximum on a pin that's doesn't mean all 23 can be at that level and is a bad idea to get to thinking you can

DC Current per I/O Pin ............................................... 40.0 mA

There even internal resistance that would limit the output of the pin but to use this is not a good idea for any one that just got started using the Arduino.
But that a whole new story.