A neutral hydrogen molecule has two protons and two electrons. If one of the electrons is removed we get a hydrogen molecular ion $(H_{2}^{+})$ . In the ground state of $H_{2}^{+}$ the two protons are separated by roughly $1.5$ $A^{o}$ and the electrons is roughly $1$ $A^{o}$ from each proton. The potential energy of the system is :

Question

Toppr Admin · Accepted Answer

The energy of the system is given by-ke2-1-5angstrom-2-k-x2212-e2-1angstrom-9-xD7-109-xD7-1010-xD7-2e2-3-x2212-2e2-9-xD7-1019-xD7-x2212-4-3-eeV-x2212-19-2eV-xA0-

The energy of the system is given by,ke2/(1.5angstrom)+2(k(−e2)/(1angstrom))=9×109×1010×(2e2/3−2e2)=9×1019×(−4/3)eeV=−19.2eV

The energy of the system is given by,
$k e^{2} / (1.5 a n g s t r o m) + 2 (k (- e^{2}) / (1 a n g s t r o m))$
$= 9 \times 10^{9} \times 10^{10} \times (2 e^{2} / 3 - 2 e^{2})$
$= 9 \times 10^{19} \times (- 4 / 3) e e V = - 19.2 e V$