What are the differences between stretching vibration and bending vibrations?
Stretching vibrations change bond lengths. Bending vibrations change bond angles.
Stretching Vibrations
A stretching vibration changes the bond length. There are two types of stretching vibrations.
In symmetric stretching, two or more bonds vibrate in and out together.
In asymmetric stretching, some bonds are getting shorter at the same time as others are getting longer.
Bending Vibrations
Bending vibrations change the angle between two bonds.
There are four types of bending vibration.
Scissoring is the movement of two atoms toward and away from each other.
Rocking is like the motion of a pendulum on a clock, but an atom is the pendulum and there are two instead of one.
Wagging is like the motion in which you make a "V" sign with your fingers and bend them back and forth from your wrist.
Twisting is a motion as if the atoms were walking on a treadmill.
Each type of vibration contributes to an infrared spectrum. For example, here is the spectrum of formaldehyde, H₂C=O.
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Stretching vibrations involve changes in bond lengths, where the atoms move closer together or further apart along the bond axis, while bending vibrations involve changes in bond angles, where the atoms move closer together or further apart within the plane perpendicular to the bond axis.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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