Angle between Angular Momentum and Momentum along z axis Calculator

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Schrodinger Wave Equation

Bohr's Atomic Model

Compton Effect

De Broglie Hypothesis

Distance of Closest Approach

Heisenberg's Uncertainty Principle

Important Formulas on Bohr's Atomic Model

Photo Electric Effect

Planck Quantum Theory

Rutherford Scattering

Sommerfeld Model

Structure of Atom

✖Angular Momentum along z Axis is the degree to which a body rotates, gives its angular momentum.ⓘ Angular Momentum along z Axis [L_z]			+10% -10%
✖Quantization of Angular Momentum is the rotation of the electron about its own axis, contributes towards an angular momentum of the electron.ⓘ Quantization of Angular Momentum [l_Quantization]			+10% -10%

✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Angle between Angular Momentum and Momentum along z axis [θ]

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Formula

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Angle between Angular Momentum and Momentum along z axis

Formula

`"θ" = acos("L"_{"z"}/"l"_{"Quantization"})`

Example

`"89.93489°"=acos("0.025"/"22")`

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Angle between Angular Momentum and Momentum along z axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theta = acos(Angular Momentum along z Axis/Quantization of Angular Momentum)
θ = acos(L_z/l_Quantization)
This formula uses 2 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
Angular Momentum along z Axis - Angular Momentum along z Axis is the degree to which a body rotates, gives its angular momentum.
Quantization of Angular Momentum - Quantization of Angular Momentum is the rotation of the electron about its own axis, contributes towards an angular momentum of the electron.

STEP 1: Convert Input(s) to Base Unit

Angular Momentum along z Axis: 0.025 --> No Conversion Required
Quantization of Angular Momentum: 22 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(L_z/l_Quantization) --> acos(0.025/22)

Evaluating ... ...

θ = 1.56965996291396

STEP 3: Convert Result to Output's Unit

1.56965996291396 Radian -->89.9348911456484 Degree (Check conversion here)

FINAL ANSWER

89.9348911456484 ≈ 89.93489 Degree <-- Theta

(Calculation completed in 00.004 seconds)

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National Institute of Information Technology (NIIT), Neemrana

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< 22 Schrodinger Wave Equation Calculators

Angle between Orbital Angular Momentum and z Axis

Go Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1))))

Magnetic Quantum Number given Orbital Angular Momentum

Go Magnetic Quantum Number = cos(Theta)*sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1))

Orbital Angular Momentum

Go Angular Momentum = sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1))*[hP]/(2*pi)

Spin Angular Momentum

Go Angular Momentum = sqrt(Spin Quantum Number*(Spin Quantum Number+1))*[hP]/(2*pi)

Angle between Angular Momentum and Momentum along z axis

Go Theta = acos(Angular Momentum along z Axis/Quantization of Angular Momentum)

Relation between Magnetic Angular Momentum and Orbital Angular Momentum

Go Angular Momentum along z Axis = Quantization of Angular Momentum*cos(Theta)

Magnetic Quantum Angular Momentum

Go Angular Momentum along z Axis = (Magnetic Quantum Number*[hP])/(2*pi)

Spin only Magnetic Moment

Go Magnetic Moment = sqrt((4*Spin Quantum Number)*(Spin Quantum Number+1))

Magnetic Moment

Go Magnetic Moment = sqrt(Quantum Number*(Quantum Number+2))*1.7

Angular Momentum using Quantum Number

Go Angular Momentum = (Quantum Number*[hP])/(2*pi)

Exchange Energy

Go Exchange Energy = (Number of Electron*(Number of Electron-1))/2

Number of Spherical Nodes

Go Number of Nodes = Quantum Number-Azimuthal Quantum Number-1

Number of Peaks Obtained in Curve

Go Number of Peaks = Quantum Number-Azimuthal Quantum Number

Energy of Electron by Principal Quantum Number

Go Energy = Quantum Number+Azimuthal Quantum Number

Number of Orbitals in Sub Shell of Magnetic Quantum Number

Go Total Number of Orbitals = (2*Azimuthal Quantum Number)+1

Total Magnetic Quantum Number Value

Go Magnetic Quantum Number = (2*Azimuthal Quantum Number)+1

Maximum Number of Electrons in Sub Shell of Magnetic Quantum Number

Go Number of Electron = 2*((2*Azimuthal Quantum Number)+1)

Number of Orbitals of Magnetic Quantum Number in Main Energy Level

Go Total Number of Orbitals = (Number of Orbits^2)

Total Number of Orbitals of Principal Quantum Number

Go Total Number of Orbitals = (Number of Orbits^2)

Spin Multiplicity

Go Spin Multiplicity = (2*Spin Quantum Number)+1

Maximum Number of Electron in Orbit of Principal Quantum Number

Go Number of Electron = 2*(Number of Orbits^2)

Total Number of Nodes

Go Number of Nodes = Quantum Number-1

Angle between Angular Momentum and Momentum along z axis Formula

Theta = acos(Angular Momentum along z Axis/Quantization of Angular Momentum)
θ = acos(L_z/l_Quantization)

What is quantum number?

Quantum Number is the set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. There are four quantum numbers, namely, principal, azimuthal, magnetic and spin quantum numbers. The values of the conserved quantities of a quantum system are given by quantum numbers. An electron in an atom or ion has four quantum numbers to describe its state and yield solutions to the Schrödinger wave equation for the hydrogen atom.

How to Calculate Angle between Angular Momentum and Momentum along z axis?

Angle between Angular Momentum and Momentum along z axis calculator uses Theta = acos(Angular Momentum along z Axis/Quantization of Angular Momentum) to calculate the Theta, The Angle between Angular Momentum and Momentum along z axis formula is defined as the angle along the z-axis of the vector inclined with the angular momentum vector. Theta is denoted by θ symbol.

How to calculate Angle between Angular Momentum and Momentum along z axis using this online calculator? To use this online calculator for Angle between Angular Momentum and Momentum along z axis, enter Angular Momentum along z Axis (L_z) & Quantization of Angular Momentum (l_Quantization) and hit the calculate button. Here is how the Angle between Angular Momentum and Momentum along z axis calculation can be explained with given input values -> 5152.89 = acos(0.025/22).

FAQ

What is Angle between Angular Momentum and Momentum along z axis?

The Angle between Angular Momentum and Momentum along z axis formula is defined as the angle along the z-axis of the vector inclined with the angular momentum vector and is represented as θ = acos(L_z/l_Quantization) or Theta = acos(Angular Momentum along z Axis/Quantization of Angular Momentum). Angular Momentum along z Axis is the degree to which a body rotates, gives its angular momentum & Quantization of Angular Momentum is the rotation of the electron about its own axis, contributes towards an angular momentum of the electron.

How to calculate Angle between Angular Momentum and Momentum along z axis?

The Angle between Angular Momentum and Momentum along z axis formula is defined as the angle along the z-axis of the vector inclined with the angular momentum vector is calculated using Theta = acos(Angular Momentum along z Axis/Quantization of Angular Momentum). To calculate Angle between Angular Momentum and Momentum along z axis, you need Angular Momentum along z Axis (L_z) & Quantization of Angular Momentum (l_Quantization). With our tool, you need to enter the respective value for Angular Momentum along z Axis & Quantization of Angular Momentum and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Theta?

In this formula, Theta uses Angular Momentum along z Axis & Quantization of Angular Momentum. We can use 1 other way(s) to calculate the same, which is/are as follows -

Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1))))

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