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Consider the spacing of vibrational energy levels of materials X and Al based on the quantum harmonic oscillator model for interatomic bonds. X is a hypothetical material of stiffness ks = 2N/m and atomic mass 200 mN (where mN is the mass of a nucleon). The interatomic stiffness of Al is ks = 17N/m, and its atomic mass is 27 mN. What is the ratio of the energy level spacings, ∆EX ∆EAl ?

Answer :

Answer:

The ratio is [tex]R = 0.126[/tex]

Explanation:

From the question we are told that

         The stiffness is [tex]K_s = 2 N /m[/tex]

          The  atomic mass is [tex]A_t = 200mN[/tex]

          The inter-atomic stiffness of Al is [tex]K_s__{AI}} = 17 N/m[/tex]

          The atomic mass of  AI is [tex]A_t__{AI}} = 27 mN[/tex]

The ratio of the energy is mathematically represented as

         [tex]R = \sqrt{(\frac{K_s__{X}}{A_t__{X}}} )*(\frac{ A_t__{AI}}{ K_s__{AI}} })}[/tex]

         [tex]R = \sqrt{(\frac{2}{200} )*(\frac{ 27}{ 17 } )}[/tex]

             [tex]R = 0.126[/tex]

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