Finding the Spring Constant - Help Algebra Issues

[courtney1121]

Finding the Spring Constant -- Help! Algebra Issues!

Molecular bonds can be treated like springs. From the vibrational frequencies of the bonds, one can determine the appropriate spring constants. Hydrogen, H2, has a vibrational frequency of 1.3192 X 1014Hz. Deuterium, D2, is an isotope of hydrogen and is twice as massive as hydrogen. It has a vibrational frequency of 0.9345 X 1014Hz. Do these molecules have the same spring constant? Explain.

I used the equations

T=2pi * square root m/k
F = 1/T

From the second equation, I got T=1/F. Since I know F of both bonds, I can find T.

For H2, T = 7.58X10^-15 and for D2 T= 1.07X10^-14.

mass for H2 is just m and mass for D2 is 2m

I plugged all these expressions into T=2pi*square root m/k, and isolated k, and got H2 to equal 6.87X10^29 and D2 to be 6.896X10^29. So they are only about .03 off which I think is pretty close to having pretty much the same spring constant. What I had problems with, was I am not sure whether I did the correct algebra for isolating k. Also, does it seem like I am approaching this problem correctly? Thanks!

 

[radou]

Your approach looks okay, and the solution should be too, under the assumption you did the algebra correctly and plugged in the appropriate masses of the isotopes.

 

[m2003]

As a scientist, it appears that you have approached this problem correctly. Your use of the equations and solving for k seems to be correct. However, to confirm your answer, I would suggest checking your calculations and units to ensure they are accurate and consistent. Additionally, it may be helpful to compare your results to known values for the spring constant of H2 and D2 to see if they are within a reasonable range. Overall, your approach and reasoning seem sound, but it is always important to double check your work and use known values for comparison. Good luck!