Finding the Spring Constant - Help Algebra Issues

In summary, the vibrational frequencies of hydrogen and deuterium can be used to determine their respective spring constants, and in this case, they are very similar. However, there may be some discrepancies due to possible errors in the algebraic calculations.
  • #1
courtney1121
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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!
 
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  • #2
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.
 
  • #3


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!
 

Related to Finding the Spring Constant - Help Algebra Issues

1. What is the spring constant and why is it important?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It tells us how much force is required to stretch or compress the spring by a certain distance. This constant is important because it allows us to predict and understand the behavior of a spring in various situations.

2. How do I find the spring constant of a spring?

The spring constant can be found by dividing the force applied to the spring by the resulting change in length or displacement. This can be represented by the equation: k = F/x, where k is the spring constant, F is the force applied, and x is the displacement of the spring.

3. What are the units for spring constant?

The units for spring constant depend on the units used for force and displacement. In the SI system, the units for spring constant are newtons per meter (N/m). In the imperial system, the units are pounds per inch (lb/in).

4. Can the spring constant change?

Yes, the spring constant can change depending on factors such as the material, length, and diameter of the spring, as well as the temperature and the amount of force applied. The spring constant can also change if the spring is stretched beyond its elastic limit, causing it to permanently deform.

5. How does the spring constant affect the behavior of a spring?

The spring constant directly affects the amount of force required to stretch or compress a spring. A higher spring constant means the spring is stiffer and requires more force to change its length. This also means that the spring will resist changes in its length more strongly, leading to a stronger restoring force and a smaller displacement. On the other hand, a lower spring constant results in a less stiff spring that is easier to stretch or compress.

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