Hi, Not a good circuit. So lets clarify a few things first, one is it an N-channel mosfet or a bipolar transistor? The symbol used is for a bipolar transistor which is why I ask. If it is an enhancement mode n-channel MOSFET then the diode is not needed since the parasitic diode in the MOSFET will provide the necessary protection, but lets get to that.
The diode in the case of a bipolar transistor is to prevent the collector/emitter pair from becoming reverse biased when the inductor in the solenoid generates a negative voltage potential when the transistor switches off. Based on how quickly you turn it off (and most transistors can turn off in a few tens of nanoseconds, the negative voltage that appears at the collector (or source for a MOSFET) will be -Ldi/dt where L is the inductance of the solenoid’s coil.
Without a diode between emitter and collector, (or drain and source) the collector (source) will “see” a voltage that is negative with respect to ground. That that can exceed the breakdown voltage of the emitter diode resulting in destruction of the transistor. In MOSFETs there is a parasitic diode formed between the drain and the source which will conduct that current protecting the transistor.
Generally, if you’re using an N-Channel MOSFET for this sort of circuit it is useful to have a pull down resistor on the gate. Since MOSFETs are voltage controlled devices rather than current controlled, a floating gate can accumulate charge and slowly switch on, activating your solenoid unexpectedly. But put a 10 - 50K resistor to ground from the Gate and it will keep the gate from accumulating charge and thus from turning on. For a single connection to a MOSFET you don’t actually need a resistor between the Particle board and the Gate. The current limit on the Particles I/O pins will keep it from drawing too much current when the gate is charging.