The lower energy states in a covalently bound diatomic molecule can be found approximately from the so called Morse potential U(r) U 0 (e 2(r r0) a e 2(r r0) a ), where r is the atomic separation and U 0 , r 0 , and a are constants determined from experimental data Calculate dU dr and d 2 U dr 2 to...

The Morse potential Ur is given by Ur U0e2rr0a e2rr0a To find dUdr we can use the chai ...

The lower-energy states in a covalently bound diatomic molecule can be found approximately from the so-called Morse

Question:

The lower-energy states in a covalently bound diatomic molecule can be found approximately from the so-called Morse potential U(r) = U₀(e^2(r-r0)/a - e^-2(r-r0)/a ), where r is the atomic separation and U₀, r₀, and a are constants determined from experimental data. Calculate dU/dr and d²U/dr² to show that U has a minimum, and find expressions for (a) U_min and (b) the separation r_min at the minimum energy.