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Sagot :
Answer:
radius = 37.69 mm
Explanation:
Calculate the radius a of the spherical cavity that has this property
Frequency of emission = 10 GHz
This problem is similar to infinite spherical wall potential
first step:
Express the energy eigenvalue of the system : [tex]E_{100} =E_{Is} = \frac{9.87h^2}{2ma^2}[/tex]
First excited state energy can be expressed as : E[tex]_{IP}[/tex] = 20.19 h^2 / 2ma^2
Given that the frequency of emission (γ ) = 10 GHz
next step :
calculate the energy of emitted photon ( E ) = h γ
= 6.626 * 10^-36 * 10 * 10^9
= 6.626 * 10^-24 joules
E[tex]_{IP}[/tex] - E[tex]_{IS}[/tex] = 6.626 * 10^-24
∴ a^2 = 1.42 * 10^-13 m^2
hence a = √ 1.42 * 10^-13 m^2 = 37.69 * 10^-6 m ≈ 37.69 mm
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