Moment of Inertia of dysprosium-160

AI Thread Summary
The discussion centers on calculating the moment of inertia for the dysprosium-160 nucleus, which behaves like a spinning object with quantized angular momentum. When transitioning from the l = 2 state to the l = 0 state, the nucleus emits an 87 keV photon, and the kinetic energy change is linked to the moment of inertia through the formula Change in KE = Change in L2 / 2I. An initial calculation yielded an incorrect moment of inertia value, prompting a reevaluation of the energy change, which should account for the photon emitted. The conversation emphasizes the importance of verifying calculations and understanding energy conservation in nuclear transitions.
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Homework Statement


The nucleus dysprosium-160 (containing 160 nucleons) acts like a spinning object with quantized angular momentum, L2 = l(l + 1) * h_bar2, and for this nucleus it turns out that l must be an even integer (0, 2, 4...). When a Dy-160 nucleus drops from the l = 2 state to the l = 0 state, it emits an 87 keV photon (87 ✕ 103 eV).

h_bar = reduced Planck's constant

Homework Equations



Kinetic Energy = L2 / 2I , where I is the moment of inertia

The Attempt at a Solution



Change in KE = Change in L2 / 2I = 5h_bar2 / 2I
Substituting and solving for I gave me around 2*10-54 which apparently isn't the answer.
Am I using the wrong formula?

edit: rookie mistake, Change in KE = 6 * h_bar... not 5.
 
Last edited:
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Show your reasoning. Where does the energy come from? Where does it go?
How did you account for the energy of the photon, for instance?
Check other sources of mistakes - like the value of I and the units.
 

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