Question:
In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius 'r' with speed 'v'. The magnetic moment associated with electron is
In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius 'r' with speed 'v'. The magnetic moment associated with electron is
Show Hint
The ratio of magnetic moment to angular momentum ($L = mvr$) is constant: $\frac{M}{L} = \frac{e}{2m}$.
Updated On: Apr 30, 2026
- \( \frac{evr}{3} \)
- \( \frac{evr}{2} \)
- evr
- \( \sqrt{2}evr \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
Magnetic moment ($M$) of a revolving electron is $M = I \times A$.
Step 2: Current and Area
Current $I = \frac{e}{T} = \frac{e}{(2\pi r / v)} = \frac{ev}{2\pi r}$
Area $A = \pi r^2$
Step 3: Calculation
$M = \left( \frac{ev}{2\pi r} \right) \times (\pi r^2)$
$M = \frac{evr}{2}$
Step 4: Conclusion
The magnetic moment is $\frac{evr}{2}$.
Final Answer:(B)
Magnetic moment ($M$) of a revolving electron is $M = I \times A$.
Step 2: Current and Area
Current $I = \frac{e}{T} = \frac{e}{(2\pi r / v)} = \frac{ev}{2\pi r}$
Area $A = \pi r^2$
Step 3: Calculation
$M = \left( \frac{ev}{2\pi r} \right) \times (\pi r^2)$
$M = \frac{evr}{2}$
Step 4: Conclusion
The magnetic moment is $\frac{evr}{2}$.
Final Answer:(B)
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET The Kinetic Theory of Gases Questions
- The ratio of the specific heats \( \frac{C_p}{C_v} = \gamma \) in terms of degrees of freedom 'n' is given by
- The quantity \( \frac{pV}{kT} \) represents (where \( k \) is the Boltzmann constant)
- If a gas is compressed isothermally then the r.m.s. velocity of the molecules
- The ratio of specific heat at constant pressure to specific heat at constant volume (\( \gamma \)) for a gas is \( \gamma = \left( 1 + \frac{2}{f} \right) \) where \( f \) is the number of degrees of freedom of a molecule of a gas. The ratio of \( \gamma_{r} \) for rigid diatomic to \( \gamma_{m} \) for monatomic is
- Let the r.m.s. velocity of molecules of a given mass of gas be \( C_1 \) at temperature \( 27^\circ\text{C} \). When the temperature is increased to \( 327^\circ\text{C} \), the r.m.s. velocity is \( C_2 \). Then the ratio \( \dfrac{C_2}{C_1} \) is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions