Question

The rotational constant and centrifugal correction factors for HBr are 8.473 cm-1 and 0.0003 cm-1 , respectively:

(a) What are the energies of the 3 lowest

Answer 1

lowest possible value of J is 0

given

rotational constant B=8.473 cm^-1)

centrifugal constant D=0.0003 cm^-1

Energy E₀= BJ(J+1) -DJ²(J+1 )² cm^-1

for  ^J=0

E₀= 8.473 *0 (0+1) - 0.0003*0(0+1 )² cm^-1

E₀ ^{= 0}

^{next level}

J=1

Energy E₁= BJ(J+1) -DJ²(J+1 )² cm^-1

^J=1

E₁= 8.473 *1(1+1) - 0.0003*1²(1+1 )² cm^-1

E₁⁼ 8.473 *2 - 0.0003*4 cm^-1

E₁ ⁼ 8.473 *2 - 0.0003*4 ​​​​​​​ cm^-1

E₂ ⁼ 16.946-1.2*10^-3​​​​​​​ cm^-1

E₁ ⁼ 16.9448​​​​​​​ cm^-1

^{next level}

J=2

Energy E₁= BJ(J+1) -DJ²(J+1 )² cm^-1

E₂= 8.473 *2(2+1) - 0.0003*2²(2+1 )² cm^-1

E₂⁼ 8.473 *6 - 0.0003*4*9 cm^-1

E₂ ⁼ 8.473 *6 - 0.0003*36 ​​​​​​​ cm^-1

E₂ ⁼ 50.838 - 0.0108 ​​​​​​​ cm^-1

E₂⁼ 50.8272​​​​​​​ cm^-1

the energies of the 3 lowest level of HBr are 0,16.9448​​​​​​​ cm^-1, 50.8272​​​​​​​ cm^-1