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 attched to the DNA backbone. The oscillation of the oxygen atom occurs with frequency f = 3.7 x 1013 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 for a DNA molecule after the sulfur substitution.

Explanation / Answer

f=1/(2)*(k/m)

We know the frequency=3.7*10^13

K is our unkown but remains the same for both atoms.

We know the atomic mass of Oxygen is 15.99 or about 16. Using a conversion factor we can covert amu's to kg: 1 amu=1.660538782 × 10^27

so 16.00*1.660538782 × 10^27=2.65686205*10^-26kg

Now use the formula to solve for your spring constant k.

f=1/(2)*(k/m)

3.7*10^13=1/(2)*(k/2.65686205*10^-26)            first get rid of the 1/(2)

2.324778564=)(k/2.65686205*10^-26)                  square both sides

5.404595369e28=k/2.65686205*10^-26                  multiply 2.65686205*10^-26 to both sides

k=1435.926433

Now we can use this sprink constant to work backwards with the new mass of the sulphur atom which is:

32.065amu*1.660538782 × 10^27=5.3245176*10^-26kg

f=1/(2)*(k/m)

f=1/(2)*(1435.926433/5.3245176*10^-26)

f=2.613641957*10^13 Hz

Hope this helps!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.