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Angle between Orbital Angular Momentum and z Axis Formula

GoAngle between Angular Momentum and Momentum along z axis Formula

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Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint. Check FAQs

θ = a \cos (\frac{m}{\sqrt{l \cdot (l + 1)}})

θ - Theta?m - Magnetic Quantum Number?l - Azimuthal Quantum Number?

Angle between Orbital Angular Momentum and z Axis Example

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Here is how the Angle between Orbital Angular Momentum and z Axis equation looks like with Values.

Here is how the Angle between Orbital Angular Momentum and z Axis equation looks like with Units.

Here is how the Angle between Orbital Angular Momentum and z Axis equation looks like.

88.7337 = a \cos (\frac{2}{\sqrt{90 \cdot (90 + 1)}})

88.7337° = a \cos (\frac{2}{\sqrt{90 \cdot (90 + 1)}})

88.7337 = a \cos (\frac{2}{\sqrt{90 \cdot (90 + 1)}})

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Schrodinger Wave Equation » fx Angle between Orbital Angular Momentum and z Axis

Angle between Orbital Angular Momentum and z Axis Solution

Follow our step by step solution on how to calculate Angle between Orbital Angular Momentum and z Axis?

FIRST Step Consider the formula

θ = a \cos (\frac{m}{\sqrt{l \cdot (l + 1)}})

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{2}{\sqrt{90 \cdot (90 + 1)}})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{2}{\sqrt{90 \cdot (90 + 1)}})

Next Step Evaluate

∴

θ = 1.54869474267074rad

Next Step Convert to Output's Unit

∴

θ = 88.7336725091491°

LAST Step Rounding Answer

∴

θ = 88.7337°

Angle between Orbital Angular Momentum and z Axis Formula Elements

Variables

Functions

Theta

Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Theta

Magnetic Quantum Number

Magnetic Quantum Number is the number which divides the subshell into individual orbitals which hold the electrons.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Magnetic Quantum Number

Azimuthal Quantum Number

Azimuthal Quantum Number is a quantum number for an atomic orbital that determines its orbital angular momentum.

Symbol: l

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Azimuthal Quantum Number

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Theta

Go Angle between Angular Momentum and Momentum along z axis

θ = a \cos (\frac{L z}{l Quantization})

Other formulas in Schrodinger Wave Equation category

Go Maximum Number of Electron in Orbit of Principal Quantum Number

n electron = 2 \cdot ({n orbit}^{2})

Go Total Number of Orbitals of Principal Quantum Number

t = ({n orbit}^{2})

Go Total Magnetic Quantum Number Value

m = (2 \cdot l) + 1

Go Number of Orbitals of Magnetic Quantum Number in Main Energy Level

t = ({n orbit}^{2})

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

Angle between Orbital Angular Momentum and z Axis evaluator uses Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)))) to evaluate 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 evaluate Angle between Orbital Angular Momentum and z Axis using this online evaluator? To use this online evaluator for Angle between Orbital Angular Momentum and z Axis, enter Magnetic Quantum Number (m) & Azimuthal Quantum Number (l) and hit the calculate button.

FAQs on Angle between Orbital Angular Momentum and z Axis

What is the formula to find Angle between Orbital Angular Momentum and z Axis?

The formula of Angle between Orbital Angular Momentum and z Axis is expressed as Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)))). Here is an example- 5084.065 = acos(2/(sqrt(90*(90+1)))).

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

With Magnetic Quantum Number (m) & Azimuthal Quantum Number (l) we can find Angle between Orbital Angular Momentum and z Axis using the formula - Theta = acos(Magnetic Quantum Number/(sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)))). This formula also uses Cosine (cos)Inverse Cosine (acos), Square Root (sqrt) function(s).

What are the other ways to Calculate Theta?

Here are the different ways to Calculate Theta-

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

Can the Angle between Orbital Angular Momentum and z Axis be negative?

Yes, the Angle between Orbital Angular Momentum and z Axis, measured in Angle can be negative.

Which unit is used to measure Angle between Orbital Angular Momentum and z Axis?

Angle between Orbital Angular Momentum and z Axis is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle between Orbital Angular Momentum and z Axis can be measured.

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Angle between Orbital Angular Momentum and z Axis Formula

​GoAngle between Angular Momentum and Momentum along z axis Formula

Angle between Orbital Angular Momentum and z Axis Example

Angle between Orbital Angular Momentum and z Axis Solution

Angle between Orbital Angular Momentum and z Axis Formula Elements

Other Formulas to find Theta

Other formulas in Schrodinger Wave Equation category

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

FAQs on Angle between Orbital Angular Momentum and z Axis

Variable Name

GoAngle between Angular Momentum and Momentum along z axis Formula