This probably isn't quite the question that one would expect on but i really want to know what exactly it was that i did wrong:

i was asked this question on e2020 (the e standing for education), and i was positive that i did all of the equations that i had to do right. i got the direction of r right on my first try (both ys add to zero, so the angle is automatically 0°), but i'm stumped on how i'm supposed to get 0.5n for the magnitude. if anybody knows the process that i missed, then let me know. i took a screencap of the question that this happened on for you to have a reference.

Is it possible to use the energy from two atoms colliding to create a clean burning lasting fuel source with a large amount of force? is it also possible to harness that energy from the two atoms colliding to create a clean energy source that will last for years from just two atoms colliding. is there a possibility to control and store that energy for years but slowly let the energy out enough to power cities cheaper and faster.

Acylinder with a movable piston contains 11.7 moles of a monatomic ideal gas at a pressure of 1.32×10^5 pa. the gas is initially at a temperature of 300 k. an electric heater adds 43200 j of energy into the gas while the piston moves in such a way that the pressure remains constant. cp=20.79 j k^−1 mol^−1 for a monatomic ideal gas, and that the number of gas molecules is equal to avogadro's number (6.022×10^23) times the number of moles of the gas. (a) what is the temperature of the gas after the energy is added? (b) what is the change in volume of the gas? (c) how much work is done by the gas during this process?

At very high pressures, gases become and will eventually a) more dense; become hotter b) more dense; change to a liquid or solid c) less dense; combust d) less dense; turn into a liquid