An oxygen atom at a particular site within a DNA molecule can be made to execute

Question

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 fO=3.7×1013Hz .

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.

Explanation / Answer

here,

atomic mass of sulphur , ms = 5.32 * 10^-26 kg

atomic mass of oxygen , mo = 2.657 * 10^-26 kg

fO = 3.7 * 10^13 Hz

let the spring constant be k

fO = 1/2pi * sqrt( k/mO)

3.7 * 10^13 = 1/2pi* sqrt( k /( 2.657 * 10^-26))

k = 1434.55 N/m

for sulphur

fs = 1/2pi * sqrt( 1434.55/( 5.32 * 10^-26))

fs = 2.61 * 10^13 Hz

the frequency of spring after the sulphur substitution is 2.61 * 10^13 Hz

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