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 =μR^{2}where μ is the reduced mass

μ = (m_{1}*m_{2})R^{2}

Here the molecule given is H_{2}.

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^{-12}m

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} kgm^{2}

**μ=4.66 x 10 ^{-48} kgm^{2}**

a. Calculate the angular momentum in the *J*=1 rotational
level for H_{2}

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

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

**Angular momentum = 1.49x10 ^{-34}Js**

b. Calculate the energy in the *J*=1 rotational level for
H_{2}

E = h^{2}J(J+1)/(8π^{2}I)

for J=1

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

**E = 2.39x10 ^{-21} J**

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