Answer:
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
