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uranmaximum [27]
2 years ago
8

A classical estimate of the vibrational frequency is ff = 7.0×10137.0×1013 HzHz. The mass of a hydrogen atom differs little from

the mass of a proton. If the HIHI molecule is modeled as two atoms connected by a spring, what is the force constant of the spring?
Physics
1 answer:
vlada-n [284]2 years ago
0 0

Answer:

The force constant of the spring is 317.8 N/m.

Explanation:

Given that,

Frequency f=7.0\times10^{13}\ Hz

We need to calculate the reduced mass

Using formula of reduced mass

\mu=\dfrac{m_{H}m_{I}}{m_{H}+m_{I}}

Where, m_{H}= atomic mass of H

m_{I}= atomic mass of I

Put the value into the formula

\mu=\dfrac{1\times126.9}{1+126.9}

\mu=0.99\ u

\mu=0.99\times1.66\times10^{-27}\ Kg

\mu=1.643\times10^{-27}\ kg

We need to calculate the force constant of the spring

Using formula of frequency

f=\dfrac{1}{2\pi}\times\sqrt{\dfrac{k}{\mu}}

k=f^2\times 4\pi^2\times\mu

Put the value into the formula

k=(7.0\times10^{13})^2\times4\pi^2\times1.643\times10^{-27}

k=317.8\ N/m

Hence, The force constant of the spring is 317.8 N/m.

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