Advertisements
Advertisements
Question
A uniform magnetic field B exist in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr's quantization rule for angular momentum, calculate (a) the smallest possible radius of the electron (b) the radius of the nth orbit and (c) the minimum possible speed of the electron.
Advertisements
Solution
According to Bohr's quantization rule,
`mvr = (nh)/(2pi)`
'r' is minimum when 'n' has minimum value, i.e. 1.
`mv = (nh)/(2pir)` ........(1)
Again,` r = (mv)/(qB)`
`rArr mv = rqB` .........(2)
From (1) and (2), we get
`rqB = (nh)/(2pir) ` [From (1)]
`rArr r^2 = (nh)/(2pieB)` [∴q=e ]
`rArr r = sqrt((h)/(2pieB)` [n = 1]
(b) For the radius of nth orbit,
`r = sqrt((nh)/(2pieB)`
`(C) mvr = (nh)/(2pi), r = (mv)/(qB)`
Substituting the value of 'r' in (1), we get
`mvxx(mv)/(qB)=(nh)/(2pi)`
`rArr m ^2v^2 = (heB)/(2pi)` [n=1,q=e]
`v^2 = (heB)/(2pim^2)`
`v = sqrt((heB)/(2pim^2)`
APPEARS IN
RELATED QUESTIONS
Define ionization energy.
Calculate the shortest wavelength of the spectral lines emitted in Balmer series.
[Given Rydberg constant, R = 107 m–1]
Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n − 1). For large n, show that this frequency equals the classical frequency of revolution of the electron in the orbit.
How would the ionization energy change when the electron in the hydrogen atom is replaced by a particle of mass 200 times that of the electron but having the same charge?
The simple Bohr model is not applicable to He 4 atom because ______.
- He4 is an inert gas.
- He4 has neutrons in the nucleus.
- He4 has one more electron.
- electrons are not subject to central forces.
Imagine removing one electron from He4 and He3. Their energy levels, as worked out on the basis of Bohr model will be very close. Explain why.
A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the nth orbit and the particle’s speed v in the orbit depend on n as ______.
Who explained the quantisation of the orbiting electron’s angular momentum in 1923?
Under what conditions can particle waves produce standing waves?
Which wavelengths survive in a plucked string?
Which expression is de Broglie’s relation for wavelength?
When can the magnitude of the electron’s momentum be written as \[mv_n\]?
What is the electron’s de Broglie wavelength when its momentum magnitude is \[mv_n\]?
For which atoms does Bohr’s model correctly predict gross features?
Which radiation frequencies does Bohr’s model predict especially well for hydrogenic atoms?
Which electrical force is included in the Bohr model?
What property of spectral lines can Bohr’s model not explain, despite predicting frequencies for hydrogenic atoms?
