Which Formula Correctly Represents the Kinetic Orbital Momentum of an Electron?

In summary, the conversation discusses the two equations for the kinetic orbital momentum of an electron in an atom, with one coming from quantum mechanics and the other from Bohr's theory. The speaker is confused about which equation is correct and asks for clarification.
  • #1
C_Ovidiu
23
0
In some places I saw that the module of the kinetic orbital momentum of an electron in an atom is
a) L^2=l(l+1)h^/(4pi^2) ==> L =h/(2pi)sqrt(l*(l+1)) l=0,1,2,...n-1
b) L=n*h/(2pi)
n beeing the energy level of an electron .

Now , my opinion is that the first is true . But I saw some problems solved using only the second value . I'm really confused . Which one is it ?
Thank you !
 
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  • #2
Well, the first equation comes from the angular momentum theory in quantum mechanics, while the second is nothing but one of Bohr's postulates in his 1913 theory of the hydrogen atom.

Do you see what the difference is really about ?
 
Last edited:
  • #3
Tks .
There are lots of differences .
 

1. What is kinetic orbital momentum?

Kinetic orbital momentum, also known as angular momentum, is a physical quantity that describes the rotational motion of an object around a fixed point or axis. It is a vector quantity that depends on the mass, velocity, and distance of an object from the axis of rotation.

2. How is kinetic orbital momentum calculated?

Kinetic orbital momentum is calculated by multiplying the mass of an object by its velocity and the distance from the axis of rotation, and then taking the cross product of these values. The formula for calculating kinetic orbital momentum is L = mvr, where L is the angular momentum, m is the mass, v is the velocity, and r is the distance from the axis of rotation.

3. What are the units of kinetic orbital momentum?

The units of kinetic orbital momentum are kilogram-meter squared per second (kg·m2/s). This unit is a combination of the units for mass, velocity, and distance, as seen in the formula L = mvr.

4. How is kinetic orbital momentum related to torque?

Kinetic orbital momentum is related to torque, as torque is the rate of change of angular momentum. This means that the more torque applied to an object, the faster its angular momentum will change. Similarly, the greater the angular momentum of an object, the more torque is required to change its rotation.

5. What are some real-life examples of kinetic orbital momentum?

A spinning top, a rotating planet, and a spinning ice skater are all examples of kinetic orbital momentum in action. In each of these cases, the objects have a fixed axis of rotation and are experiencing a combination of mass, velocity, and distance from the axis, resulting in a non-zero angular momentum. In more complex systems, such as the rotation of a planet around the sun, the concept of kinetic orbital momentum is used to explain and predict the behavior of celestial bodies.

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