Question

Assume that in the Stern-Gerlach experiment for neutral silver atoms, the magnetic field has a magnitude of B = 0.50 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?

Answer 1

Given Data

Magnitude of the magnetic field is B = 0.5 T

We have

?_B = Bohr Magneton = 9.27* 10^-24 J / T

h = Plancks constant = 6.625*10^-34 J s

c = speed of light = 3*10⁸ m/s

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a )

    Energy difference ? E = 2?_B B

                                       = 2 * ( 9.27* 10^-24 J / T ) ( 0.5 T )

                                       = 9.27* 10^-24 J

                                        = 9.27* 10^-24 J / 1.6*10^-19 J / eV

                                        = 5.79*10^-5e V

                                         = 57.9375 *10^-6 e V

                                         = 57.94 ? e V --> Answer

b )   frequency f   =? E / h

                          =   9.27* 10^-24 J / T / 6.625*10^-34 J s

                         = 1.4*10¹⁰Hz

                         = 14 *10⁹ Hz

                         = 14 GHz --> Answer

c ) Wavelength ? = c /f

                            = 3*10⁸ m/s / 1.4*10¹⁰ Hz

                            = 0.021 m

                            = 2.1 cm --> Answer

d) Thsi radiation belongs to short wave region --> Answer