Where can I purchase a thermocouple for a Rheem 50 gallon hot water heater? The pilot light will not stay lit, so this is the most likely thing to change, right?

The system I am familiar with uses a vapour pressure type thermocouple and if the pilot remains lit the thermocouple is working as it controls the gas for the pilot and the burner at the same time from the same source - if the gas control is ok and the flow isn't prevented by the thermostat then if the pilot remains alight, there should be a flow of gas and the burner should light - unless the gas jet is blocked or something else, some other type of blockage is preventing the flow of gas to the burner...

I suggest you check the gas jet and the flow of gas to it...

Open following links for pilot and troubleshooting resources:
Problem could be bad thermocouple, thermocouple not sitting in pilot flame, pilot orifice needs to be cleaned, water heater needs more air, dirty air intake, hot attic environment, backdraft blowing out pilot, or bad gas control valve.
If you get flame, then ECO is not tripped.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot
http://waterheatertimer.org/How-to-test-water-heater-thermocouple.html
http://waterheatertimer.org/pdf/How-to-replace-thermocouple.pdf

If pilot lights and flame is robust and clear blue, and pilot goes out later, then some suspects can be excluded: air in gas line, low gas pressure, thermocouple is overtightened (finger-tight + 1/4 turn), thermocouple not positioned correctly in the flame, dirty pilot tube.
If flame is yellowish and small: then clean pilot tube and combustion parts.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#clean
Remaining suspects can include: air in gas line, low gas pressure, bad gas control valve, tight house so household vent fans pull air down water heater vent that blows out pilot, hot attic with inadequate ventilation, water dripping down vent.

Open following links to read troubleshoot resources.
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

Burner parts need yearly cleaning, air intake needs periodic cleaning, burner parts cannot be exposed to trace amounts of chemical without damaging parts, no water should be dripping down from vent, vent should be checked for updraft, ample combustion air is required especially in closed basements, tight houses, and hot attic, bleed gas line to remove air, check that gas control thermostat is functioning.
Open following links for pilot light help:
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf

Open following links for pilot light help:
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf
http://waterheatertimer.org/images/Negative-pressure.jpg
http://waterheatertimer.org/pdf/Bosch_Ventilating_tight_houses.pdf

Since pilot light goes out and can be re-lit, problem is probably not thermocouple, gas control valve, or air in gas line. But these things can factor in as contributing factors.
Problem is likely one of following or combination of following including dirty burner parts, tight house, incorrect vent lengths, negative pressure caused by other venting appliances, condensation dripping down into combustion area, and inadequate oxygen supply due to hot or closed-off room or attic location.

Gas water heaters draw air from surrounding area. If water heater is located inside house, then air has to enter home through cracks and when doors and windows are opened. Other gas appliances and vent fans also draw air from same indoor area. When other vent fans turn on, air can be drawn down the water heater vent and blow out pilot light.
Inspect combustion chamber to make sure there is no condensate water dripping down from incorrect vent that is putting out flame. If combustion chamber is dry, then close doors and windows. Turn on all vent fans and gas appliances that vent outdoors, and see if water heater pilot goes out.
Consult with plumber or product manual about proper horizontal and vertical lengths of vent pipe for your model. Have plumber clean combustion parts and inspect vent termination and check gas pressure and bleed gas line.
Add louver opening to outdoors so air can enter room where water heater is located.

Hopefully just the thermocouple. The thermocouple is the small rod right next to the pilot light. The flame on the pilot heats up the thermocouple and keeps the gas valve on. You can replace it yourself. The thermocouple will be connect by a small nut on the underneath side of the valve, and you will have to pull the thermocouple out of the pilot assembly. Not an expensive part, you can get it at any hardware store. Hope this helps you .

These videos should help you to a successful repair.
http://www.ehow.com/video_5238686_troubleshoot-pilot-hot-water-heater.html

http://www.ehow.com/video_5238684_install-thermocouple-water-heater.html

Thermocoupling may be bad or need to be cleaned.

The most common reason a pilot light will not stay lit is a bad thermocouple. How old is the water heater? If the pilot light will light, but then go out when you release the safety button, that is a sure sign the thermocouple is bad. You can buy a replacement thermocouple at your local home improvement store. There is a small chance that the control valve has gone bad, but that is highly unlikely.

Hi I would try changing the thermocouple