Q: The magnetic moment \$(\mu)\$ of a revolvng electron around the nucleus varies with principle quantum number n as

Magnetic moment \${\mu}\$ of a revolving electron around the nucleus \$=n\mu_B\$Where \$\mu_B=\displaystyle\frac{eh}{4\pi m}\$=Bohr Magneton.So, \$\mu \propto n\$

Q: The minimum magnetic dipole moment of electron in hydrogen atom is

\$\displaystyle I=\dfrac { ev }{ 2\pi r } \\ \mu =IA=\dfrac { ev }{ 2\pi r } \times \pi { r }^{ 2 }=\dfrac { evr }{ 2 } =\dfrac { e }{ 2m } (mvr)\\ l=mvr=\dfrac { nh }{ 2\pi } \\ \mu =\dfrac { neh }{ 4\pi m } \$ For minimum dipole moment, \$n = 1\$, which gives, \$\mu =\dfrac { eh }{ 4\pi m } \$

Q: Relation between magnetic moment and angular velocity is

Magnetic moment,\$M = Ia = l(\pi r^{2}) = \dfrac {q}{T}\times \pi r^{2} (\because q = lt)\$.As, \$\omega = \dfrac {2\pi}{T}\$\$\therefore M = \dfrac {q\omega r^{2}}{2}\$\$\Rightarrow M \propto \omega\$

Question 1

The magnetic moment $(\mu)$ of a revolvng electron around the nucleus varies with principle quantum number n as

Accepted Answer

Magnetic moment ${\mu}$ of a revolving electron around the nucleus $=n\mu_B$Where $\mu_B=\displaystyle\frac{eh}{4\pi m}$=Bohr Magneton.So, $\mu \propto  n$

Question 2

The minimum magnetic dipole moment of electron in hydrogen atom is

Accepted Answer

$\displaystyle I=\dfrac { ev }{ 2\pi r } \ \mu =IA=\dfrac { ev }{ 2\pi r } \times \pi { r }^{ 2 }=\dfrac { evr }{ 2 } =\dfrac { e }{ 2m } (mvr)\ l=mvr=\dfrac { nh }{ 2\pi  } \ \mu =\dfrac { neh }{ 4\pi m } $ For minimum dipole moment, $n = 1$, which gives, $\mu =\dfrac { eh }{ 4\pi m } $

Question 3

Relation between magnetic moment and angular velocity is

Accepted Answer

Magnetic moment,$M = Ia = l(\pi r^{2}) = \dfrac {q}{T}\times \pi r^{2} (\because q = lt)$.As, $\omega = \dfrac {2\pi}{T}$$\therefore M = \dfrac {q\omega r^{2}}{2}$$\Rightarrow M \propto \omega$

Magnetism And Matter

Physics
2022 Views

The magnetic moment $(μ)$ of a revolvng electron around the nucleus varies with principle quantum number n as

The minimum magnetic dipole moment of electron in hydrogen atom is

Relation between magnetic moment and angular velocity is

Magnetism And Matter

Physics 2022 Views

The magnetic moment (μ) of a revolvng electron around the nucleus varies with principle quantum number n as

The minimum magnetic dipole moment of electron in hydrogen atom is

Relation between magnetic moment and angular velocity is

Physics
2022 Views

The magnetic moment $(μ)$ of a revolvng electron around the nucleus varies with principle quantum number n as