JEE Exam  >  JEE Questions  >  In an experiment electrons are accelerated, f... Start Learning for Free
In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.
[Charge of the electron = 1.6 × 10–19 C Mass of the electron = 9.1 × 10–31 kg]
  • a)
    7.5 × 10–4 m
  • b)
    7.5 × 10–3 m
  • c)
    7 .5 m
  • d)
    7.5 × 10–2 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In an experiment electrons are accelerated, from rest, by applying a v...


View all questions of this test
Most Upvoted Answer
In an experiment electrons are accelerated, from rest, by applying a v...
To calculate the radius of the path, we can use the formula for the radius of a charged particle moving in a magnetic field:

r = (m*v) / (q*B)

Where:
r is the radius of the path
m is the mass of the electron (9.11 x 10^-31 kg)
v is the velocity of the electron
q is the charge of the electron (1.6 x 10^-19 C)
B is the magnetic field strength (100 mT = 0.1 T)

First, let's calculate the velocity of the electron:
The voltage applied to accelerate the electron is 500 V. We can use the equation for the electric potential energy to find the kinetic energy of the electron:

KE = q * V

KE = (1.6 x 10^-19 C) * (500 V)
KE = 8 x 10^-17 J

The kinetic energy of the electron can also be written as:

KE = (1/2) * m * v^2

8 x 10^-17 J = (1/2) * (9.11 x 10^-31 kg) * v^2

v^2 = (2 * 8 x 10^-17 J) / (9.11 x 10^-31 kg)
v^2 = 3.51 x 10^13 m^2/s^2

v = sqrt(3.51 x 10^13 m^2/s^2)
v = 5.92 x 10^6 m/s

Now we can calculate the radius of the path:
r = (m*v) / (q*B)
r = ((9.11 x 10^-31 kg) * (5.92 x 10^6 m/s)) / ((1.6 x 10^-19 C) * (0.1 T))
r = 3.42 x 10^-3 m

Therefore, the radius of the path is approximately 3.42 mm.
Free Test
Community Answer
In an experiment electrons are accelerated, from rest, by applying a v...
Explore Courses for JEE exam

Similar JEE Doubts

The orbital and spin angular momentum of the atom influence its magnetic structure and these properties are most directly studied by placing the atom in a magnetic field. Also, a magnetic field can affect the wavelengths of the emitted photons.The angular momentum vector associated with an atomic state can take up only certain specified directions in space. This concept of space quantization was shown by Otto Stern and Walthor Gerlach in their experiment.In the experiment, silver is vapourized in an electric oven and silver atoms spray into the evacuated apparatus through a small hole in the oven wall. The atoms which are electrically neutral but have a magnetic moment, are formed into a narrow beam as they pass through a slit in a screen. The beam, thus collimated, then passes between the poles of an electromagnet and finally, deposits its silver atoms on a glass plate that serves as a detector. The pole faces of the magnet are shaped to make the magnetic field as nonuniform as possible.In a non-uniform magnetic field, there is a net force on a magnetic dipole. Its magnitude and direction depends on the orientation of the dipole. Thus the silver atoms in the beam are deflected up or down, depending on the orientation of their magnetic dipole moments with respect to the z–direction.The potential energy of a magnetic dipole in a magnetic field where is magnetic dipole moment of the atom. From symmetry, the magnetic field at the beam position has no x or y components i.e.The net force Fz on the dipole isThus, the net force depends, not on the magnitude of the field itself, but on its spatial derivative or gradient.The ResultsIf space quantization did not exist, then could take on any value from + to –, the result would be a spreading out of the beam when the magnet was turned ON. However, the beam was split cleanly into two subbeams, each subbeam corresponding to one of the two permitted orientations of the magnetic moment ofthe silver atom, as shown.In a silver atom, all the spin and orbital magnetic moments of the electrons cancel, except for those of the atoms single valance electron. For this electron the orbital magnetic moment is zero because orbital angular momentum is zero (because for electrons of s–orbit, L = 0), leaving only the spin magnetic moment. This can take up only two orientations in a magnetic field, corresponding to ms = +1/2 and ms = – 1/2. Hence there are two subbeams – and not some other number.Q.A hydrogen atom in ground state passes through a magnetic field that has a gradient of 16mT/m in the vertical direction. If vertical component magnetic moment of the atom is 9.3 × 10–24 J/T, then force on it due to the magnetic moment of the electron is

The orbital and spin angular momentum of the atom influence its magnetic structure and these properties are most directly studied by placing the atom in a magnetic field. Also, a magnetic field can affect the wavelengths of the emitted photons.The angular momentum vector associated with an atomic state can take up only certain specified directions in space. This concept of space quantization was shown by Otto Stern and Walthor Gerlach in their experiment.In the experiment, silver is vapourized in an electric oven and silver atoms spray into the evacuated apparatus through a small hole in the oven wall. The atoms which are electrically neutral but have a magnetic moment, are formed into a narrow beam as they pass through a slit in a screen. The beam, thus collimated, then passes between the poles of an electromagnet and finally, deposits its silver atoms on a glass plate that serves as a detector. The pole faces of the magnet are shaped to make the magnetic field as nonuniform as possible.In a non-uniform magnetic field, there is a net force on a magnetic dipole. Its magnitude and direction depends on the orientation of the dipole. Thus the silver atoms in the beam are deflected up or down, depending on the orientation of their magnetic dipole moments with respect to the z–direction.The potential energy of a magnetic dipole in a magnetic field where is magnetic dipole moment of the atom. From symmetry, the magnetic field at the beam position has no x or y components i.e.The net force Fz on the dipole isThus, the net force depends, not on the magnitude of the field itself, but on its spatial derivative or gradient.The ResultsIf space quantization did not exist, then could take on any value from + to –, the result would be a spreading out of the beam when the magnet was turned ON. However, the beam was split cleanly into two subbeams, each subbeam corresponding to one of the two permitted orientations of the magnetic moment ofthe silver atom, as shown.In a silver atom, all the spin and orbital magnetic moments of the electrons cancel, except for those of the atoms single valance electron. For this electron the orbital magnetic moment is zero because orbital angular momentum is zero (because for electrons of s–orbit, L = 0), leaving only the spin magnetic moment. This can take up only two orientations in a magnetic field, corresponding to ms = +1/2 and ms = – 1/2. Hence there are two subbeams – and not some other number.Q.A hydrogen atom in ground state passes through a magnetic field that has a gradient of 16mT/m in the vertical direction. If vertical component magnetic moment of the atom is 9.3 × 10–24 J/T, then force on it due to the magnetic moment of the electron is

The orbital and spin angular momentum of the atom influence its magnetic structure and these properties are most directly studied by placing the atom in a magnetic field. Also, a magnetic field can affect the wavelengths of the emitted photons.The angular momentum vector associated with an atomic state can take up only certain specified directions in space. This concept of space quantization was shown by Otto Stern and Walthor Gerlach in their experiment.In the experiment, silver is vapourized in an electric oven and silver atoms spray into the evacuated apparatus through a small hole in the oven wall. The atoms which are electrically neutral but have a magnetic moment, are formed into a narrow beam as they pass through a slit in a screen. The beam, thus collimated, then passes between the poles of an electromagnet and finally, deposits its silver atoms on a glass plate that serves as a detector. The pole faces of the magnet are shaped to make the magnetic field as nonuniform as possible.In a non-uniform magnetic field, there is a net force on a magnetic dipole. Its magnitude and direction depends on the orientation of the dipole. Thus the silver atoms in the beam are deflected up or down, depending on the orientation of their magnetic dipole moments with respect to the z–direction.The potential energy of a magnetic dipole in a magnetic field where is magnetic dipole moment of the atom. From symmetry, the magnetic field at the beam position has no x or y components i.e.The net force Fz on the dipole isThus, the net force depends, not on the magnitude of the field itself, but on its spatial derivative or gradient.The ResultsIf space quantization did not exist, then could take on any value from + to –, the result would be a spreading out of the beam when the magnet was turned ON. However, the beam was split cleanly into two subbeams, each subbeam corresponding to one of the two permitted orientations of the magnetic moment ofthe silver atom, as shown.In a silver atom, all the spin and orbital magnetic moments of the electrons cancel, except for those of the atoms single valance electron. For this electron the orbital magnetic moment is zero because orbital angular momentum is zero (because for electrons of s–orbit, L = 0), leaving only the spin magnetic moment. This can take up only two orientations in a magnetic field, corresponding to ms = +1/2 and ms = – 1/2. Hence there are two subbeams – and not some other number.Q.A hydrogen atom in ground state passes through a magnetic field that has a gradient of 16mT/m in the vertical direction. If vertical component magnetic moment of the atom is 9.3 × 10–24 J/T, then force on it due to the magnetic moment of the electron is

In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer?
Question Description
In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer?.
Solutions for In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In an experiment electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied.[Charge of the electron = 1.6 × 10–19 CMass of the electron = 9.1 × 10–31 kg]a)7.5 × 10–4 mb)7.5 × 10–3 mc)7 .5 md)7.5 × 10–2 mCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev