Measuring Boltzmann constant using thermal noise
You'll need more gain than that to see 5 uVrms -- the arduino probably has a resolution of 10 bits (?), equivalent to about 5 mV. To see the signal, you'll need about 50 mV, so a gain of 10,000 is needed. The opamp's DC offset might be an issue, so just use a low value of DC gain, and bypass for AC -- that also provides your LPF. 

Now check if the opamp has enough gain*BW to do this at 50 kHz. 

If this actually works, you can then arrange to short your 100k R and do a 2nd measurement -- this would measure the opamp's noise, and you can subtract the measurements (actually sqrt(difference in squares)) to get the R's noise.