Consider the spacing of vibrational energy levels of materials X and Al based on the quantum harmonic oscillator model for interatomic bonds

Question

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 ?

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Vân Khánh 2 months 2021-07-28T07:16:55+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-28T07:18:49+00:00

    Answer:

    The ratio is R = 0.126

    Explanation:

    From the question we are told that

             The stiffness is K_s = 2 N /m

              The  atomic mass is A_t = 200mN

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

              The atomic mass of  AI is A_t__{AI}} = 27 mN

    The ratio of the energy is mathematically represented as

             R = \sqrt{(\frac{K_s__{X}}{A_t__{X}}} )*(\frac{ A_t__{AI}}{ K_s__{AI}} })}

             R = \sqrt{(\frac{2}{200} )*(\frac{ 27}{ 17 } )}

                 R = 0.126

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )