BoNUs: Hydrogen Molecule We can construct a classical model for the hydrogen mol
ID: 1660293 • Letter: B
Question
BoNUs: Hydrogen Molecule We can construct a classical model for the hydrogen molecule H2 similar to Rutherford's model of a hydrogen atom. It resembles the Lewis dot structure H:H, as shown in the figure. The bond length of H2 is 0.074 nm (a) What separation of the electrons is required for the net force on a proton to vanish? (b) There is no net force on either proton in this arrange- ment, but there is a net force on each electron. Calculate the net force. Niels Bohr suggested that this force might hold each electron in a circular orbit around the axis of the H2 molecule. What is the speed of each electron? 0.074 nmExplanation / Answer
There is force of repulsion between the two protons
Fp = kq2/l2 ; l = 0.074 nm - proton seperation.
There is force of attraction on each proton due to the presence of electrons
Force of attraction form electron on each proton
Fe = kq2/(l/2)2 +(d/2)2 = 4kq2/(l2 +d2 )
The force from each electron is along the line joining the proton and electron.
resolving the force along the protn axis and perpendicular to it, the perpendicular components form each electron are in opposite directions and cancle up the parallel componenets addup
Force on each proton due to the electrons
= Fe *l/(l2 +d2)1/2
For the net force on the protns to be zero the force of repulaasion the that of attraction must be equal
kq2/l2 = 4kq2/(l2 +d2 ) * 2l/(l2 +d2)1/2
simplifying the above we get
d2 = 3l2
d = 0.128 nm
b) the net force on each electron :
Force of repulsion between the elctrons
= kq2/d2
The force of atraction between electron and proton exist, the componenets prallel to the proton axis cancel up and that perpendicular to the axis addup
= 2Fe * d/(l2 +d2)1/2
Net force on the eelctrons
= kq2/d2 - 4kq2/(l2 +d2 ) * d/(l2 +d2)1/2 - repulsive
= -2.243E-8 N ( put values k = 9.0E+9 , q = 1.8E-19, l = 0.074nm, d = 0.128 nm)
The forece is attractive since the sign is -ve.