Question

the potential energy of hydrogen atoms separated by a large distance x is given by U(x)= -C_6/x^6, where C_6 is a positive constant and equal to 4*10^-12 N*m^7. Find the force on x in Newtons at x=2cm

Answer 1

The force on x at x=2cm can be calculated by taking the derivative of the potential energy function with respect to x. The force is found to be 0.036 N.

Step-by-step explanation:

The force on x can be found by taking the negative derivative of the potential energy function with respect to x. In this case, U(x) = -C_6/x^6. Taking the derivative of this function yields the force F(x) = 6C_6/x^7. Plugging in the given value of x=2cm and the value of C_6, we can calculate the force on x.

First, we need to convert 2cm to meters by dividing by 100: 2cm = 0.02m.

Now, plugging in the values:

F(x) = 6(4*10^-12 N*m^7)/(0.02m)^7 = 0.036 N