Question

a) Calculate the angular momentum in the J=1 rotational level for H2 , which has a bond length of 74.13 pm .

b) Calculate the energy in the J=1 rotational level for H2 , which has a bond length of 74.13 pm .

please show all steps to both parts

Answer 1

Moment of inertia =μR²where μ is the reduced mass

μ = (m₁*m₂)R²

Here the molecule given is H₂.

1 amu = 1.66 x10^-27 kg

m1=m2 = mass of hydrogen = 1.007 amu = 1.007 x 1.66 x10^-27 kg

R = Bond length = 74.13 pm = 74.13 x 10^-12m

μ = (1.007 x 1.66 x10^-27 kg) x (1.007 x 1.66 x10^-27 kg)/(1.007 x 1.66 x10^-27 kg)² = 4.66 x 10^-48 kgm²

μ=4.66 x 10^-48 kgm²

a. Calculate the angular momentum in the J=1 rotational level for H₂

Angular momentum = SQRT(J(J+1)) h/(2xπ) = SQRT(2)x h/(2xπ )

= 1.41 x 6.625x10^-34 Js/(2x3.14) = 1.49x10^-34Js

Angular momentum = 1.49x10^-34Js

b. Calculate the energy in the J=1 rotational level for H₂

E = h²J(J+1)/(8π²I)

for J=1

E = (6.625x10^-34 Js)² 1(2)/(8x(3.14)²x4.66 x 10^-48kgm²) = 2.39x10^-21 J

E = 2.39x10^-21 J