Magnetic Quantum Number given Orbital Angular Momentum Solution

STEP 0: Pre-Calculation Summary
Formula Used
Magnetic Quantum Number = cos(Theta)*sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1))
m = cos(θ)*sqrt(l*(l+1))
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)
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
Magnetic Quantum Number - Magnetic Quantum Number is the number which divides the subshell into individual orbitals which hold the electrons.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
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
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Azimuthal Quantum Number: 90 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
m = cos(θ)*sqrt(l*(l+1)) --> cos(0.5235987755982)*sqrt(90*(90+1))
Evaluating ... ...
m = 78.3741028656788
STEP 3: Convert Result to Output's Unit
78.3741028656788 --> No Conversion Required
FINAL ANSWER
78.3741028656788 78.3741 <-- Magnetic Quantum Number
(Calculation completed in 00.004 seconds)

Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Pragati Jaju
College Of Engineering (COEP), Pune
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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

Magnetic Quantum Number given Orbital Angular Momentum Formula

Magnetic Quantum Number = cos(Theta)*sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1))
m = cos(θ)*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 Magnetic Quantum Number given Orbital Angular Momentum?

Magnetic Quantum Number given Orbital Angular Momentum calculator uses Magnetic Quantum Number = cos(Theta)*sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)) to calculate the Magnetic Quantum Number, The Magnetic quantum number given orbital angular momentum formula is defined as the number which divides the subshell into individual orbitals which hold the electrons. Magnetic Quantum Number is denoted by m symbol.

How to calculate Magnetic Quantum Number given Orbital Angular Momentum using this online calculator? To use this online calculator for Magnetic Quantum Number given Orbital Angular Momentum, enter Theta (θ) & Azimuthal Quantum Number (l) and hit the calculate button. Here is how the Magnetic Quantum Number given Orbital Angular Momentum calculation can be explained with given input values -> 78.3741 = cos(0.5235987755982)*sqrt(90*(90+1)).

FAQ

What is Magnetic Quantum Number given Orbital Angular Momentum?
The Magnetic quantum number given orbital angular momentum formula is defined as the number which divides the subshell into individual orbitals which hold the electrons and is represented as m = cos(θ)*sqrt(l*(l+1)) or Magnetic Quantum Number = cos(Theta)*sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)). Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint & Azimuthal Quantum Number is a quantum number for an atomic orbital that determines its orbital angular momentum.
How to calculate Magnetic Quantum Number given Orbital Angular Momentum?
The Magnetic quantum number given orbital angular momentum formula is defined as the number which divides the subshell into individual orbitals which hold the electrons is calculated using Magnetic Quantum Number = cos(Theta)*sqrt(Azimuthal Quantum Number*(Azimuthal Quantum Number+1)). To calculate Magnetic Quantum Number given Orbital Angular Momentum, you need Theta (θ) & Azimuthal Quantum Number (l). With our tool, you need to enter the respective value for Theta & 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 Magnetic Quantum Number?
In this formula, Magnetic Quantum Number uses Theta & Azimuthal Quantum Number. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Magnetic Quantum Number = (2*Azimuthal Quantum Number)+1
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