Question

Calculate the reduced mass of H-atom and H2-molecule​

Answer 1

Answer:

1) Reduced mass ( ) = m1 m2 / m1+m2.

2) Moment of inertial =I = R^2 = 8.35x 10^-28 x (75.69 x 10^-12)^2 = 4.78 x 10^-48 kg m^2.

3) Angular momentum = sqrt (h / 2 * J (J+1)). = 1.49 x 10^-34 JS.

4) E =( h^2 / 8 ^2 R^2 ) J (J+1) we have J=1.

5) E = h^2 / 4 ^2 I.

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Answer 2

Reduced mass is the representation of a two-body system as a single-body one. when the motion of two bodies are only under mutual interactions, the inertial mass of the moving body with respect to the body at rest can be simplified to a reduced mass.

reduced mass of H-atom :

$μ = m1*m2 / m1+m2$

$μ = me / (1+me/mp)$

$μ =0.06% me$

$me = 9.1 * 10^-31kg$

$mp = 1.6 * 10^-27kg$

Reduced mass of H2 molecule :

let us consider a hydrogen atom of mass 1.01g/mol another hydrogen atom of 1.01g/mol

$μ = 1.01 *1.01 / 1.01+1.01$

$μ = 1.01/2 g/mol$