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Angle between Orbital Angular Momentum and z Axis Calculator

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✖Magnetic Quantum Number is the number which divides the subshell into individual orbitals which hold the electrons.ⓘ Magnetic Quantum Number [m]			+10% -10%
✖Azimuthal Quantum Number is a quantum number for an atomic orbital that determines its orbital angular momentum.ⓘ Azimuthal Quantum Number [l]			+10% -10%

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

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Angle between Orbital Angular Momentum and z Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1))))
θ = acos(m/(sqrt(l*(l+1))))
This formula uses 3 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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(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.
Magnetic Quantum Number - Magnetic Quantum Number is the number which divides the subshell into individual orbitals which hold the electrons.
Azimuthal Quantum Number - Azimuthal Quantum Number is a quantum number for an atomic orbital that determines its orbital angular momentum.

STEP 1: Convert Input(s) to Base Unit

Magnetic Quantum Number: 2 --> No Conversion Required
Azimuthal Quantum Number: 90 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(m/(sqrt(l*(l+1)))) --> acos(2/(sqrt(90*(90+1))))

Evaluating ... ...

θ = 1.54869474267074

STEP 3: Convert Result to Output's Unit

1.54869474267074 Radian -->88.7336725091491 Degree (Check conversion here)

FINAL ANSWER

88.7336725091491 ≈ 88.73367 Degree <-- Theta

(Calculation completed in 00.004 seconds)

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< Schrodinger Wave Equation Calculators

Total Magnetic Quantum Number Value

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

Number of Orbitals of Magnetic Quantum Number in Main Energy Level

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

Total Number of Orbitals of Principal Quantum Number

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

Maximum Number of Electron in Orbit of Principal Quantum Number

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

Angle between Orbital Angular Momentum and z Axis Formula

LaTeX Go

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

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 Orbital Angular Momentum and z Axis?

Angle between Orbital Angular Momentum and z Axis calculator uses Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)))) to calculate the Theta, The Angle between orbital angular momentum and 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 Orbital Angular Momentum and z Axis using this online calculator? To use this online calculator for Angle between Orbital Angular Momentum and z Axis, enter Magnetic Quantum Number (m) & Azimuthal Quantum Number (l) and hit the calculate button. Here is how the Angle between Orbital Angular Momentum and z Axis calculation can be explained with given input values -> 5084.065 = acos(2/(sqrt(90*(90+1)))).

FAQ

What is Angle between Orbital Angular Momentum and z Axis?

The Angle between orbital angular momentum and 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(m/(sqrt(l*(l+1)))) or Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)))). Magnetic Quantum Number is the number which divides the subshell into individual orbitals which hold the electrons & Azimuthal Quantum Number is a quantum number for an atomic orbital that determines its orbital angular momentum.

How to calculate Angle between Orbital Angular Momentum and z Axis?

The Angle between orbital angular momentum and 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(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)))). To calculate Angle between Orbital Angular Momentum and z Axis, you need Magnetic Quantum Number (m) & Azimuthal Quantum Number (l). With our tool, you need to enter the respective value for Magnetic Quantum Number & Azimuthal Quantum Number 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 Magnetic Quantum Number & Azimuthal Quantum Number. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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