Calculating Charge Needed for Same Binding Energy in H2+

[ghallya]

hi I need help in solving this

The protons the H2+ molculer ion are 0.106 nm apart and the binding energy of H2+ is 2.65 ev , what negetive charge must be placed halfway between two protons this distance apart to give the same binding energy?

I calculated it for the electrons , but here i didn know for the protons ?
I tryed to use the graph I had but I don't think its the right solution
so if someone could help me or give an equation I could apply

thanx

 

[maverick280857]

Please correct me if I'm wrong...

The two protons repel each other so left to itself, the two proton system is electrostatically unstable. You need a negative charge somewhere between them so that they are both attracted to the -ve charge and effectively stay in place. The binding energy is now defined in terms of the 3 charge system: 2 protons + 1 negative charge. [No other nuclear force is being considered for the mathematical calculations]

Does this help?

PS--Show your work

 

[kyle8921]

To calculate the charge needed for the same binding energy in H2+, we can use the equation for Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

In this case, we know the distance between the two protons (0.106 nm) and the desired binding energy (2.65 eV). We also know that the charge of an electron is -1.602 x 10^-19 Coulombs.

Using the equation F = k(q1q2)/r^2, where F is the force, k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the two particles, and r is the distance between them, we can calculate the charge needed for the same binding energy.

First, we need to convert the binding energy from eV to Joules. 1 eV is equal to 1.602 x 10^-19 Joules, so the binding energy in Joules is 2.65 x 1.602 x 10^-19 = 4.249 x 10^-19 Joules.

Next, we plug in the values into the equation: 4.249 x 10^-19 = (8.99 x 10^9)(q1)(1.602 x 10^-19)/(0.106 x 10^-9)^2.

Solving for q1, we get q1 = 6.153 x 10^-19 Coulombs.

Therefore, the negative charge needed to be placed halfway between the two protons to give the same binding energy is 6.153 x 10^-19 Coulombs, which is approximately -3.83 times the charge of an electron.

I hope this helps! Please let me know if you have any further questions.