The potential energy (V) of a system is modeled as a function of the interatomic distance (R). The equilibrium interatomic distance (Re) is the distance at which the first derivative of the potential energy (∂V/∂R) is equal to zero. Of the choices given, equation B correctly models Re as the distance where the first derivative of V is equal to zero.

1. some
bonds angles dihedrals
⎛ Ai A j Bi B j qi q j ⎞
atoms atoms
∑ k (r − r ) ∑ k (θ − θ i,e ) + ∑ Vi cos (φi ) + ∑ ∑ ⎜ − r 6 + r12 + r ⎟
2 2
V= i i i,e + i i
i i i i j ⎝ ij ij ij ⎠
Hvilken
ligning
er
korrekt
for
CH4?
A. V = 4kCH ( rCH − rCH ,e ) + 4kHCH (θ HCH − θ HCH ,e )
2 2
⎛ qH qH AH AH BH BH ⎞
B. V = 4kHH ( rHH − rHH ,e ) + 4kHCH (θ HCH − θ HCH ,e )
2 2
+ 6⎜ − 6 + 12 ⎟
⎝ rHH rHH rHH ⎠
⎛ qH qH AH AH BH BH ⎞
C. V = 4kHH ( rHH − rHH ,e ) + 6kHCH (θ HCH − θ HCH ,e )
2 2
+ 16 ⎜ − 6 + 12 ⎟
⎝ rHH rHH rHH ⎠

2. some
bonds angles dihedrals
⎛ Ai A j Bi B j qi q j ⎞
atoms atoms
∑ k (r − r ) ∑ k (θ − θ i,e ) + ∑ Vi cos (φi ) + ∑ ∑ ⎜ − r 6 + r12 + r ⎟
2 2
V= i i i,e + i i
i i i i j ⎝ ij ij ij ⎠
Hvilken
ligning
er
korrekt
for
CH4?
A. V = 4kCH ( rCH − rCH ,e ) + 4kHCH (θ HCH − θ HCH ,e )
2 2
⎛ qH qH AH AH BH BH ⎞
B. V = 4kHH ( rHH − rHH ,e ) + 4kHCH (θ HCH − θ HCH ,e )
2 2
+ 6⎜ − 6 + 12 ⎟
⎝ rHH rHH rHH ⎠
⎛ qH qH AH AH BH BH ⎞
C. V = 4kHH ( rHH − rHH ,e ) + 6kHCH (θ HCH − θ HCH ,e )
2 2
+ 16 ⎜ − 6 + 12 ⎟
⎝ rHH rHH rHH ⎠

3. some
bonds angles dihedrals atoms atoms ⎛ Ai A j Bi B j qi q j ⎞
∑ k (r − r ) ∑ k (θ − θ i,e ) + ∑ Vi cos (φi ) + ∑ ∑ ⎜ − r 6 + r12 + r ⎟
2 2
V= i i i,e + i i
i i i i j ⎝ ij ij ij ⎠
Hvilken
ligning
er
korrekt
for
H2O2?
⎛q q B B ⎞ ⎛q q B B ⎞
A. V = 2kHO ( rHO − rHO,e ) + kOO ( rOO − rOO,e ) + ⎜ H H − H6 H + H12 H ⎟ + 2 ⎜ H O − H6 O + H12 O ⎟
2 2 A A A A
⎝ rHH rHH rHH ⎠ ⎝ rHO rHO rHO ⎠
B. V = 2kHO ( rHO − rHO,e ) + kOO ( rOO − rOO,e ) + 2kHOH (θ HOH − θ HOH ,e )
2 2 2
C. V = 2kHO ( rHO − rHO,e ) + kOO ( rOO − rOO,e ) + 2kHOO (θOOH − θOOH ,e ) +
2 2 2 qH qH AH AH BH BH
− 6 + 12
rHH rHH rHH

4. some
bonds angles dihedrals atoms atoms ⎛ Ai A j Bi B j qi q j ⎞
∑ k (r − r ) ∑ k (θ − θ i,e ) + ∑ Vi cos (φi ) + ∑ ∑ ⎜ − r 6 + r12 + r ⎟
2 2
V= i i i,e + i i
i i i i j ⎝ ij ij ij ⎠
Hvilken
ligning
er
korrekt
for
H2O2?
⎛q q B B ⎞ ⎛q q B B ⎞
A. V = 2kHO ( rHO − rHO,e ) + kOO ( rOO − rOO,e ) + ⎜ H H − H6 H + H12 H ⎟ + 2 ⎜ H O − H6 O + H12 O ⎟
2 2 A A A A
⎝ rHH rHH rHH ⎠ ⎝ rHO rHO rHO ⎠
B. V = 2kHO ( rHO − rHO,e ) + kOO ( rOO − rOO,e ) + 2kHOH (θ HOH − θ HOH ,e )
2 2 2
C. V = 2kHO ( rHO − rHO,e ) + kOO ( rOO − rOO,e ) + 2kHOO (θOOH − θOOH ,e ) +
2 2 2 qH qH AH AH BH BH
− 6 + 12
rHH rHH rHH

5. V (R) = k ( R − Re )
1 2
2
Hvilken
ligning
er
korrekt?
⎛ ∂V ⎞
A. Re = Rg + k ⎜
⎝ ∂ R ⎟ R= Rg
⎠
1 ⎛ ∂V ⎞
B. Re = Rg − ⎜ ⎟
k ⎝ ∂ R ⎠ R= Rg
⎛ ∂ 2V ⎞
C. Re = Rg − k ⎜ 2 ⎟
⎝ ∂ R ⎠ R= Rg

6. V (R) = k ( R − Re )
1 2
2
Hvilken
ligning
er
korrekt?
⎛ ∂V ⎞
A. Re = Rg + k ⎜
⎝ ∂ R ⎟ R= Rg
⎠
1 ⎛ ∂V ⎞
B. Re = Rg − ⎜ ⎟
k ⎝ ∂ R ⎠ R= Rg
⎛ ∂ 2V ⎞
C. Re = Rg − k ⎜ 2 ⎟
⎝ ∂ R ⎠ R= Rg

7. 1 ⎛ ∂V ⎞
V (R) = k ( R − Re )
2
1 Re = Rg − ⎜ ⎟
2 k ⎝ ∂ R ⎠ R= Rg
Hvilken
ligning
er
korrekt?
⎛ ∂ 3V ⎞
A. Re = Rg − ⎜ 3 ⎟
⎝ ∂ R ⎠ R= Rg
⎛ ∂ 2V ⎞ ⎛ ∂V ⎞
B. Re = Rg + ⎜ 2 ⎟ ⎜ ⎟
⎝ ∂ R ⎠ R= Rg ⎝ ∂ R ⎠ R= Rg
−1
⎛∂ V⎞ 2
⎛ ∂V ⎞
C. Re = Rg − ⎜ 2 ⎟ ⎜ ⎟
⎝ ∂ R ⎠ R= Rg ⎝ ∂ R ⎠ R= Rg

8. 1 ⎛ ∂V ⎞
V (R) = k ( R − Re )
2
1 Re = Rg − ⎜ ⎟
2 k ⎝ ∂ R ⎠ R= Rg
Hvilken
ligning
er
korrekt?
⎛ ∂ 3V ⎞
A. Re = Rg − ⎜ 3 ⎟
⎝ ∂ R ⎠ R= Rg
⎛ ∂ 2V ⎞ ⎛ ∂V ⎞
B. Re = Rg + ⎜ 2 ⎟ ⎜ ⎟
⎝ ∂ R ⎠ R= Rg ⎝ ∂ R ⎠ R= Rg
−1
⎛∂ V⎞ 2
⎛ ∂V ⎞
C. Re = Rg − ⎜ 2 ⎟ ⎜ ⎟
⎝ ∂ R ⎠ R= Rg ⎝ ∂ R ⎠ R= Rg