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30 August, 00:23

Assume that in the Stern-Gerlach experiment for neutral silver atoms, the magnetic field has a magnitude of B = 0.21 T. (a) What is the energy difference between the magnetic moment orientations of the silver atoms in the two subbeams? (b) What is the frequency of the radiation that would induce a transition between these two states? (c) What is the wavelength of this radiation, and (d) to what part of the electromagnetic spectrum does it belong?

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  1. 30 August, 03:37
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    Explanation

    Assume that in the Stern-Gerlach experiment for neutral silver atoms, the magnetic field has a magnitude of B = 0.21 T

    A. To calculate the energy difference in the magnetic moment orientation

    ∆E = 2μB

    For example, any electron's magnetic moment is measured to be 9.284764*10^-24 J/T

    Then

    μ = 9.284764 * 10^-24 J/T

    ∆E = 2μB

    ∆E = 2 * 9.284764 * 10^-24 * 0.21

    ∆E = 3.8996 * 10^-24 J

    Then, to eV

    1eV = 1.602 * 10^-19J

    ∆E = 3.8996 * 10^-24 J * 1eV / 1.602 * 10^-19J

    ∆E = 2.43 * 10^-5 eV

    B. Frequency?

    To determine the frequency of radiation hitch would induce the transition between the two states is,

    ∆E = hf

    Where h is plank constant

    h = 6.626 * 10-34 Js

    Then, f = ∆E / h

    f = 3.8996 * 10^-24 / 6.626 * 10^-34

    f = 5.885 * 10^9 Hz

    f ≈ 5.89 GHz

    C. The wavelength of the radiation

    From wave equation

    v = fλ

    In electromagnetic, we deal with speed of light, v = c

    And the speed of light in vacuum is

    c = 3 * 10^8 m/s

    c = fλ

    λ = c / f

    λ = 3 * 10^8 / 5.885 * 10^9

    λ = 0.051 m

    λ = 5.1 cm

    λ = 51 mm

    D. It belongs to the microwave

    From table

    Micro waves ranges from

    •Wavelength 10 to 0.01cm

    Then we got λ = 5.1 cm, which is in the range.

    •Frequency 3GHz to 3 Thz

    Then, we got f ≈ 5.89 GHz, which is in the range

    •Energy 10^-5 to 0.01 eV

    We got ∆E = 2.43 * 10^-5 eV, which is in the range of the microwave

    The value above is in microwave range
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