What to look for when selecting an RF detector diode
In RF components, you'll typically see actual frequencies and bandwidths specified, as well as matching guarantees.  At the very least, if bandwidths aren't given, you'd expect upper limits on carrier lifetime. 

A leaded diode like your 1N916 is already pretty bad at 1 GHz (being a radiator of energy and badly matchable to any microstrip line on your board), but at 2.4 GHz, that wire simply becomes a component that you'd have to calculate with.

So, that shape of diode is a basically a non-starter. All microwave circuit boards these days are SMD. How will you do a matched connection with a through-hole component if the wavelength of the signal of interest is in the same order of magnitude as the leads on that component?

Then, RF detection at 2.4 GHz is more often than not really not done with a simple diode – you actually want a mixer, because the effort of building a suitable filter that surpresses everything above your detected signal becomes pretty complex – 2.4 GHz will just see a bunch of lossy capacitors where you see an inductor.

Also, with a single diode detector, you can only detect amplitude modulations – phase is not detectable. That wastes a lot of spectrum, which is why none of the standards that actually used at 2.4 GHz these days do that. Instead, superhet or homodyne mixing receivers are employed – and the diode nonlinear that you're using for detection here is then part of the actual mixer, which typically is active.