The potential energy of a pair of hydrogen atoms separated by a large distance x is given by u(x)=−c6/x6, where c6 is a positive constant. is this force attractive or repulsive?

We need to see what happens to the energy depending on their distance. If the atoms get closer, we have that x gets smaller and their energy smaller; 1/x^6 is getting bigger but accounting for the minus sign, u gets smaller. If their distance increases, x gets bigger and similarly u increases. The forces act in a way to decrease potential energy, in every case of power. In this case, since potential energy is reduced when distance is decreased, we have that the force is attractive.

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