How can I draw a simple energy profile for an exothermic reaction in which 100 kJ mol-1 is evolved, and which has an activation energy of 50 kJmol-1?

You can start with a generic potential energy diagram for an exothermic reaction.

A reaction is defined as exothermic if you put in less energy to break the bonds of the reactants - the is the activation energy - than it is released when the products are formed.

So, the activation energy is the minimum amount of energy required for a reaction to take place. In your case, you need at least #"50 kJ/mol"# of energy to get the reaction going.

The heat evolved during the reaction, #DeltaH#, will be negative because the products are at a lower energy level than the reactants. In your case, the heat released will be

#DeltaH = "- 100 kJ/mol"#

Here's what an energy diagram for such a reaction could look like

I've assumed the energy level of the reactants to be #"200 kJ"#. The activation energy will make the energy of the reaction peak at #"250 kJ"#; the energy level of the products will be lower than that of the products by #"100 kJ"#, the heat evolved during the reaction.

In an exothermic reaction, the products will always be lower in energy than the reactants; in this case, the products are at #"100 kJ"#, #"100 kJ"# lower than what the energy of the reactants was.