Question

# a) Calculate the angular momentum in the J=1 rotational level for H2 , which has a...

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

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

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