Question

Problem 18.37

Part A

Calculate the reduced mass for H2, which has a bond length of 75.69 pm .

Part B

Calculate the moment of inertia for H2, which has a bond length of 75.69 pm .

Part C

Calculate the angular momentum in the J=1 rotational level for H2, which has a bond length of 75.69 pm .

Part D

Calculate the energy in the J=1 rotational level for H2, which has a bond length of 75.69 pm .

Answer 1

Part A

reduced mass ( $\mu$ ) =    m1 m2 / m1+m2

          =   (1.67 x 10^-27 )^2 / 2 x 1.67 x 10^-27 = 1 x 1 / 1+1 = 8.35x 10^-28 kg

Part B

Calculate the moment of inertia for H2, which has a bond length of 75.69 pm .

R = 75.69 pm = 75.69 x 10^-12 m

moment of inertial =I = $\mu$ R^2 = 8.35x 10^-28 x (75.69 x 10^-12)^2 = 4.78 x 10^-48 kg m^2

Part C

angular momentum = sqrt (h / 2 $\pi$ * J (J+1)). = 1.49 x 10^-34 JS

Part D

E =( h^2 / 8 $\pi$ ^2 $\mu$ R^2 ) J (J+1)   we have J=1

E = h^2 / 4 $\pi$ ^2 I

     = (6.625 x 10^-34 )^2 / 4 x 3.14 x 3.14 x 4.78 x 10^-48

     = 2.33 x 10^-21 J