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23 Nov 2019
Many diatomic (two-atom) molecules are bound together by covalentbonds that are much stronger than the van der Waals interaction.Examples include H2,O2 and N2 . Experiment shows that for many suchmolecules, the interaction can be described by a force of theform
F(r)=A[e^-2b(r-R0) - e^-b(r-R0)]
where A and b are positive constants, r is the center-to-centerseparation of the atoms, and R0 is the equilibrium separation. Forthe hydrogen molecule A=2.97*10^-8 N ,b= 1.95*10^10 m^-1 andR0=7.4*10^-11 m .
Fnd the force constant for small oscillations around equilibrium.(Hint: Use the expansion for e^x=1+x +\frac{x^2}{2}+ \cdots, when xis small.)
Many diatomic (two-atom) molecules are bound together by covalentbonds that are much stronger than the van der Waals interaction.Examples include H2,O2 and N2 . Experiment shows that for many suchmolecules, the interaction can be described by a force of theform
F(r)=A[e^-2b(r-R0) - e^-b(r-R0)]
where A and b are positive constants, r is the center-to-centerseparation of the atoms, and R0 is the equilibrium separation. Forthe hydrogen molecule A=2.97*10^-8 N ,b= 1.95*10^10 m^-1 andR0=7.4*10^-11 m .
Fnd the force constant for small oscillations around equilibrium.(Hint: Use the expansion for e^x=1+x +\frac{x^2}{2}+ \cdots, when xis small.)
