Question

$\textbf{Stern-Gerlach Experiment}$. In a Stern-Gerlach experiment, the deflecting force on the atom is $F$$_z$ = -$\mu$$_z$($dB$$_z$/$dz$), where $\mu$$_z$ is given by Eq. (41.38) and $dB$$_z$/$dz$ is the magnetic-field gradient. In a particular experiment, the magnetic-field region is 50.0 cm long; assume the magnetic-field gradient is constant in that region. A beam of silver atoms enters the magnetic field with a speed of 375 m/s. What value of $dB$$_z$/$d$$_z$ is required to give a separation of 1.0 mm between the two spin components as they exit the field? ($Note$: The magnetic dipole moment of silver is the same as that for hydrogen, since its valence electron is in an $l$ = 0 state.)

Name: Problem 56, Chapter 41: University Physics with Modern Physics
Uploaded: 2020-11-07T12:41:42-08:00
Duration: 6 min 31 s
Channel: Khoobchandra Agrawal

   $\textbf{Stern-Gerlach Experiment}$. In a Stern-Gerlach experiment, the deflecting force on the atom is $F$$_z$ = -$\mu$$_z$($dB$$_z$/$dz$), where $\mu$$_z$ is given by Eq. (41.38) and $dB$$_z$/$dz$ is the magnetic-field gradient. In a particular experiment, the magnetic-field region is 50.0 cm long; assume the magnetic-field gradient is constant in that region. A beam of silver atoms enters the magnetic field with a speed of 375 m/s. What value of $dB$$_z$/$d$$_z$ is required to give a separation of 1.0 mm between the two spin components as they exit the field? ($Note$: The magnetic dipole moment of silver is the same as that for hydrogen, since its valence electron is in an $l$ = 0 state.)

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 41, Problem 56

Instant Answer

Solved by Expert Khoobchandra Agrawal

11/07/2020

Step 1

This can be done using the formula for time, which is distance divided by speed. In this case, the distance is 50 cm (or 0.5 m) and the speed is 375 m/s. So, the time is given by: \[t = \frac{x}{v} = \frac{0.5}{375} = 1.33 \times 10^{-3} \, \text{s}\] Show more…

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$\textbf{Stern-Gerlach Experiment}$. In a Stern-Gerlach experiment, the deflecting force on the atom is $F$$_z$ = -$\mu$$_z$($dB$$_z$/$dz$), where $\mu$$_z$ is given by Eq. (41.38) and $dB$$_z$/$dz$ is the magnetic-field gradient. In a particular experiment, the magnetic-field region is 50.0 cm long; assume the magnetic-field gradient is constant in that region. A beam of silver atoms enters the magnetic field with a speed of 375 m/s. What value of $dB$$_z$/$d$$_z$ is required to give a separation of 1.0 mm between the two spin components as they exit the field? ($Note$: The magnetic dipole moment of silver is the same as that for hydrogen, since its valence electron is in an $l$ = 0 state.)