If one of the two electrons of a H2 molecule is removed, we get a hydrogen molecular ion Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.. In the ground state of an Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '., the two protons are separated by roughly 1.5Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '., and the electron is roughly 1Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

Asked by Topperlearning User | 22nd Apr, 2015, 07:50: AM

Expert Answer:

The system of two protons and one electron is represented in the given figure.

Charge on proton 1, q1 = 1.6 x 10-19 C

Charge on proton 2, q2 = 1.6 x 10-19 C

Charge on electron, q3 = -1.6 x 10-19 C

Distance between protons 1 and 2, d1 = 1.5 x 10-10 m

Distance between proton 1 and electron, d2 = 1 x 10-10 m

Distance between proton 2 and electron, d3 = 1 x 10-10 m

The potential energy at infinity is zero.

potential energy of the system,

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Substituting Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

begin mathsize 11px style straight V space equals space fraction numerator 9 space cross times space 10 to the power of 9 space cross times space 10 to the power of negative 19 end exponent space cross times 10 to the power of negative 19 end exponent space space over denominator 10 to the power of negative 10 end exponent end fraction open square brackets fraction numerator left parenthesis 1.6 space cross times space minus 1.6 right parenthesis over denominator 1.5 end fraction plus left parenthesis 1.6 right parenthesis squared plus left parenthesis 1.6 space cross times negative 1.6 right parenthesis squared close square brackets
straight V space equals space fraction numerator 9 space cross times space 10 to the power of 9 space cross times space left parenthesis 1.6 space cross times space 10 to the power of negative 19 end exponent right parenthesis squared over denominator 10 to the power of negative 10 end exponent end fraction open square brackets negative 1 space plus space fraction numerator 1 over denominator 1.5 end fraction space minus 1 close square brackets
straight V space equals space minus 19.2 space eV end style

Therefore, the potential energy of the system is - 19.2 eV.

Answered by  | 22nd Apr, 2015, 09:50: AM