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If one of the two electrons of a H_2 molecule is removed, we get a hydrogen molecular ion H_2^(+).In the ground state of an H_2^(+), the two protons are separated by roughly 1.5 Å, and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy. |
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Answer» SOLUTION :If zero of the potential energy is taken at infinity, then in PRESENT set up the potential energy of the system should be `U = 1/(4pi epsi_0)[(q_1q_2)/r_12 + (q_1q_3)/r_13+ (q_2q_3)/(r_23)]` `= 9 XX 10^9 [((+1.60xx10^(-19))(1.60 xx 10^(-19)))/(1.5 xx 10^(-10))+((1.60 xx 10^(-19))(-1.60 xx 10^(-19)))/(1 xx 10^(-10))+((1.60 xx 10^(-19))(-1.60xx10^(-19)))/(1 xx 10^(-10))]J` `=3.072 xx 10^(-18)J =-(3.072 xx 10^(-18))/(1.60 xx 10^(-19)) eV = -19.2eV`. 
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