Vibrational energy level calculation question
Hi guys,
I'm a first year chemistry undergrad student and was just wondering if anyone could help me with this particular question. After staring at it for the last few days with absolutely no idea on how to approach it I'd really appreciate some help! I've attached the question so any pointers or even a step-by-step guide if I'm lucky from someone would be great!
Thanks
The vibrational energy levels E(n) of a diatomic molecule is reasonably well described by:
E(n) = (n + 1/2)hv - (n + 1/2)^2 xhv, n = 0, 1, 2...
with h > 0 being Planck's constant, and x > 0 and v > 0 characterize the vibration of the molecule. If n exceeds a given value, the vibrational energy dissociates the molecule. Assuming n can adopt any value, 0 ≤ n < ∞ find the extremal points of E(n) and determine their nature. Hence evaluate the dissociation energy D(e) for the molecule. Find D(e) for the HCl molecule, for which v = 8.9875 x 10^13Hz and x = 1.74 x 10^-2.
I'm a first year chemistry undergrad student and was just wondering if anyone could help me with this particular question. After staring at it for the last few days with absolutely no idea on how to approach it I'd really appreciate some help! I've attached the question so any pointers or even a step-by-step guide if I'm lucky from someone would be great!
Thanks
The vibrational energy levels E(n) of a diatomic molecule is reasonably well described by:
E(n) = (n + 1/2)hv - (n + 1/2)^2 xhv, n = 0, 1, 2...
with h > 0 being Planck's constant, and x > 0 and v > 0 characterize the vibration of the molecule. If n exceeds a given value, the vibrational energy dissociates the molecule. Assuming n can adopt any value, 0 ≤ n < ∞ find the extremal points of E(n) and determine their nature. Hence evaluate the dissociation energy D(e) for the molecule. Find D(e) for the HCl molecule, for which v = 8.9875 x 10^13Hz and x = 1.74 x 10^-2.
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Original post by withoutlies
Hi guys,
I'm a first year chemistry undergrad student and was just wondering if anyone could help me with this particular question. After staring at it for the last few days with absolutely no idea on how to approach it I'd really appreciate some help! I've attached the question so any pointers or even a step-by-step guide if I'm lucky from someone would be great!
Thanks
The vibrational energy levels E(n) of a diatomic molecule is reasonably well described by:
E(n) = (n + 1/2)hv - (n + 1/2)^2 xhv, n = 0, 1, 2...
with h > 0 being Planck's constant, and x > 0 and v > 0 characterize the vibration of the molecule. If n exceeds a given value, the vibrational energy dissociates the molecule. Assuming n can adopt any value, 0 ≤ n < ∞ find the extremal points of E(n) and determine their nature. Hence evaluate the dissociation energy D(e) for the molecule. Find D(e) for the HCl molecule, for which v = 8.9875 x 10^13Hz and x = 1.74 x 10^-2.
I'm a first year chemistry undergrad student and was just wondering if anyone could help me with this particular question. After staring at it for the last few days with absolutely no idea on how to approach it I'd really appreciate some help! I've attached the question so any pointers or even a step-by-step guide if I'm lucky from someone would be great!
Thanks
The vibrational energy levels E(n) of a diatomic molecule is reasonably well described by:
E(n) = (n + 1/2)hv - (n + 1/2)^2 xhv, n = 0, 1, 2...
with h > 0 being Planck's constant, and x > 0 and v > 0 characterize the vibration of the molecule. If n exceeds a given value, the vibrational energy dissociates the molecule. Assuming n can adopt any value, 0 ≤ n < ∞ find the extremal points of E(n) and determine their nature. Hence evaluate the dissociation energy D(e) for the molecule. Find D(e) for the HCl molecule, for which v = 8.9875 x 10^13Hz and x = 1.74 x 10^-2.
Intergrate from zero point energy to the dissociation limit which should be n=infinity to give the dissociation energy
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