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 ?

Answer 1

The ratio is
`R = 0.126`

Step-by-step 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{((K_s__(X))/(A_t__(X))} )*(( A_t__(AI))/( K_s__(AI)) })}`

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

`R = 0.126`