- #1
courtney1121
- 68
- 0
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!
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!