Book edition 7th

Author(s) Douglas C. Giancoli

Pages 978 pages

ISBN 978-0321625922

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Short Answer

An oxygen atom at a particular site within a DNA molecule can be made to execute simple harmonic motion when illuminated by infrared light. The oxygen atom is bound with a spring-like chemical bond to a phosphorus atom, which is rigidly attached to the DNA backbone. The oscillation of the oxygen atom occurs with frequency \(f = 3.7 \times {10^{13}}\;{\rm{Hz}}\). If the oxygen atom at this site is chemically replaced with a sulfur atom, the spring constant of the bond is unchanged (sulfur is just below oxygen in the Periodic Table). Predict the frequency after the sulfur substitution.

The frequency after the sulfur substitution is \({f_{\rm{S}}} = 2.6 \times {10^{13}}\;{\rm{Hz}}\).

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Concept of relation of frequency with the mass

In order to predict the frequency after the sulfur substitution, the formula of frequency along with mass and spring constant will be utilized.

Given data

The frequency of oxygen atom is \({f_{\rm{O}}} = 3.7 \times {10^{13}}\;{\rm{Hz}}\).

The standard value of the mass of oxygen is \({m_{\rm{O}}} = 16\;{\rm{u}}\) and the mass of sulfur is \({m_{\rm{S}}} = 32\;{\rm{u}}\).

Calculation of frequency of sulfur atom

The relation of frequency and mass is calculated as:

\(\begin{aligned}{c}f &= \frac{1}{{2{\rm{\pi }}}}\sqrt {\frac{k}{m}} \\\frac{k}{{{\rm{4}}{{\rm{\pi }}^2}}} &= {f^2}m\\{f^2}m &= {\rm{constant}}\end{aligned}\)

Here, m is the mass and k is the spring constant.

The frequency of sulfur atom is calculated as:

\(\begin{aligned}{c}f_{\rm{O}}^2{m_{\rm{O}}} &= f_{\rm{S}}^2{m_{\rm{S}}}\\{f_{\rm{S}}} &= {f_{\rm{O}}}\sqrt {\frac{{{m_{\rm{O}}}}}{{{m_{\rm{S}}}}}} \\{f_{\rm{S}}} &= \left( {3.7 \times {{10}^{13}}\;{\rm{Hz}}} \right)\sqrt {\frac{{16\;{\rm{u}}}}{{32\;{\rm{u}}}}} \\{f_{\rm{S}}} &= 2.6 \times {10^{13}}\;{\rm{Hz}}\end{aligned}\)

Hence, the frequency of sulfur atom is \(2.6 \times {10^{13}}\;{\rm{Hz}}\).

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Physics Principles with Applications

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Concept of relation of frequency with the mass

Given data

Calculation of frequency of sulfur atom

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Physics Principles with Applications

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Short Answer

Step by Step Solution

Concept of relation of frequency with the mass

Given data

Calculation of frequency of sulfur atom

Most popular questions for Physics Textbooks

When the speed of your car is doubled, by what factor does its kinetic energy increase?

(I) Three forces are applied to a tree sapling, as shown in Fig. 9–46, to stabilize it. If \({\vec F_{\rm{A}}}=385\;{\rm{N}}\) and \({\vec F_{\rm{B}}} = 475\;{\rm{N}}\), find \({\vec F_{\rm{C}}}\) in magnitude and direction.

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