
If the magnetic moment of ${{\left[ Ag{{\left( CN \right)}_{2}} \right]}^{-1}}$ is zero, then the number of unpaired electrons will be:
A) 1
B) 2
C) 3
D) Zero
Answer
164.1k+ views
Hint: Magnetic moment is a way to express the paramagnetism of a coordination compound in terms of Bohr magneton. As it is the property of paramagnetism, the central metal ion must have some unpaired electrons in its valence shell to get the value. If the value of the magnetic moment is zero, it depicts the diamagnetic nature of the complex.
Formula Used:$\mu =\sqrt{n\left( n+2 \right)}\ \ \text{BM}$, where \[\mu \] is the magnetic moment, n is the number of unpaired electrons and BM (Bohr magneton) is the unit of the magnetic moment.
Complete answer:Magnetic moment is a term used in coordination chemistry to get information about the complex related to oxidation number and stereochemistry of the central metal ion. It is also used to determine the paramagnetism of a coordination complex and can be calculated if the number of unpaired electrons is known.
As per the data given in the question, the Magnetic moment of the given complex ${{\left[ Ag{{\left( CN \right)}_{2}} \right]}^{-1}}$ is zero, so according to the given formula of magnetic moment, the number of unpaired electrons can be calculated as follows:
$\mu =\sqrt{n\left( n+2 \right)}\ \ \text{BM}$
$\Rightarrow 0=\sqrt{n\left( n+2 \right)}$
Squaring both sides of the equation:
$\Rightarrow n\left( n+2 \right)=0$
As per the above equation, the possible values of n are as follows:
$\Rightarrow n=0\ ;\ n=-2$
As the number of unpaired electrons cannot be negative. Therefore, the number of unpaired electrons for the given complex is zero.
Option ‘D’ is correctoption (D) is correct.
Note: We can calculate the number of unpaired electrons using an alternative way i.e., by calculating the oxidation state of the silver ion and then, applying the valence bond theory to get the actual number of unpaired electrons as shown below:
Electronic configuration of $Ag=\ \left[ Kr \right]4{{d}^{10}}5{{s}^{1}}$
The oxidation state of silver ion: $+1$
Electronic configuration of $A{{g}^{+}}=\ \left[ Kr \right]4{{d}^{10}}5{{s}^{0}}$
So, all the electrons in the valence d orbitals are paired. Thus, the complex consists of zero unpaired electrons.
Formula Used:$\mu =\sqrt{n\left( n+2 \right)}\ \ \text{BM}$, where \[\mu \] is the magnetic moment, n is the number of unpaired electrons and BM (Bohr magneton) is the unit of the magnetic moment.
Complete answer:Magnetic moment is a term used in coordination chemistry to get information about the complex related to oxidation number and stereochemistry of the central metal ion. It is also used to determine the paramagnetism of a coordination complex and can be calculated if the number of unpaired electrons is known.
As per the data given in the question, the Magnetic moment of the given complex ${{\left[ Ag{{\left( CN \right)}_{2}} \right]}^{-1}}$ is zero, so according to the given formula of magnetic moment, the number of unpaired electrons can be calculated as follows:
$\mu =\sqrt{n\left( n+2 \right)}\ \ \text{BM}$
$\Rightarrow 0=\sqrt{n\left( n+2 \right)}$
Squaring both sides of the equation:
$\Rightarrow n\left( n+2 \right)=0$
As per the above equation, the possible values of n are as follows:
$\Rightarrow n=0\ ;\ n=-2$
As the number of unpaired electrons cannot be negative. Therefore, the number of unpaired electrons for the given complex is zero.
Option ‘D’ is correctoption (D) is correct.
Note: We can calculate the number of unpaired electrons using an alternative way i.e., by calculating the oxidation state of the silver ion and then, applying the valence bond theory to get the actual number of unpaired electrons as shown below:
Electronic configuration of $Ag=\ \left[ Kr \right]4{{d}^{10}}5{{s}^{1}}$
The oxidation state of silver ion: $+1$
Electronic configuration of $A{{g}^{+}}=\ \left[ Kr \right]4{{d}^{10}}5{{s}^{0}}$
So, all the electrons in the valence d orbitals are paired. Thus, the complex consists of zero unpaired electrons.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Types of Solutions

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 12 Chemistry Chapter 1 Solutions

Solutions Class 12 Notes: CBSE Chemistry Chapter 1

NCERT Solutions for Class 12 Chemistry Chapter 6 Haloalkanes and Haloarenes

NCERT Solutions for Class 12 Chemistry Chapter 2 Electrochemistry

Electrochemistry Class 12 Notes: CBSE Chemistry Chapter 2
