Hi. The purpose of the diode is to prevent the back EMF as you have stated, given that it's a coil driven component.
The data sheet for the part is:
The sheet indicated an average coil resistance of 42R +- 6R. This would create a current of 5V/42R = 119mA, which is too high for the pins of the uC.
While pg 316 the ATmega 644 Datasheet of indicates that the absolute maximum rating of DC Current per I/O pin is 40mA, it also states that
"Stresses beyond those listed under “Absolute
Maximum Ratings” may cause permanent damage
to the device. This is a stress rating only and
functional operation of the device at these or
other conditions beyond those indicated in the
operational sections of this specification is not
implied. Exposure to absolute maximum rating
conditions for extended periods may affect
So I like to keep current draw per pin at 20-35 mA, thus to reduce the current, I would use a resistor of 220R. 5V/220 = 22mA, which is ideal to me. However to reduce the noise while I breadboard, I overspecc'ed R16 to lower the volume.