Question #2025

The fundamental frequency of 2D [sup]35[/sup]Cl is 2.090x10[sup]5[/sup] 1/m. Calculate its force constant.

Expert's answer

As the fundamental frequency equals to

<img src="/cgi-bin/mimetex.cgi?%5Cnu%20=%20%5Cfrac%7B1%7D%7B2%5Cpi%20c%7D%20%5Csqrt%7B%5Cfrac%7Bf%28m_1%20+m_2%29%7D%7Bm_1%20m_2%7D%7D" title="\nu = \frac{1}{2\pi c} \sqrt{\frac{f(m_1 +m_2)}{m_1 m_2}}">,

let's find the force

<img src="https://latex.codecogs.com/gif.latex?2.09%20%5Ctimes%2010%5E3%20=%20%5Cfrac%7B1%7D%7B2%5Cpi%5Ccdot%203%20%5Ctimes%2010%5E8%7D%5Csqrt%7B%5Cfrac%7B1225f%7D%7B70%7D%7D%20%5C%5C%202.09%20%5Ctimes%2010%5E3%20=%202.22%20%5Ctimes%2010%5E%7B-9%7D%20%5Csqrt%7Bf%7D%20%5C%5C%20f%20=%208.86%20%5Ctimes%2010%5E%7B23%7D" title="2.09 \times 10^3 = \frac{1}{2\pi\cdot 3 \times 10^8}\sqrt{\frac{1225f}{70}} \\ 2.09 \times 10^3 = 2.22 \times 10^{-9} \sqrt{f} \\ f = 8.86 \times 10^{23}">

<img src="/cgi-bin/mimetex.cgi?%5Cnu%20=%20%5Cfrac%7B1%7D%7B2%5Cpi%20c%7D%20%5Csqrt%7B%5Cfrac%7Bf%28m_1%20+m_2%29%7D%7Bm_1%20m_2%7D%7D" title="\nu = \frac{1}{2\pi c} \sqrt{\frac{f(m_1 +m_2)}{m_1 m_2}}">,

let's find the force

<img src="https://latex.codecogs.com/gif.latex?2.09%20%5Ctimes%2010%5E3%20=%20%5Cfrac%7B1%7D%7B2%5Cpi%5Ccdot%203%20%5Ctimes%2010%5E8%7D%5Csqrt%7B%5Cfrac%7B1225f%7D%7B70%7D%7D%20%5C%5C%202.09%20%5Ctimes%2010%5E3%20=%202.22%20%5Ctimes%2010%5E%7B-9%7D%20%5Csqrt%7Bf%7D%20%5C%5C%20f%20=%208.86%20%5Ctimes%2010%5E%7B23%7D" title="2.09 \times 10^3 = \frac{1}{2\pi\cdot 3 \times 10^8}\sqrt{\frac{1225f}{70}} \\ 2.09 \times 10^3 = 2.22 \times 10^{-9} \sqrt{f} \\ f = 8.86 \times 10^{23}">

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