Moment of Inertia of dysprosium-160

In summary, the conversation discusses the behavior of a dysprosium-160 nucleus and how it emits an 87 keV photon when transitioning from a specific state to another. The nucleus has quantized angular momentum and its moment of inertia can be calculated using the formula L2 = l(l + 1) * h_bar^2. However, in the attempt to find the moment of inertia, the individual made a mistake in using the formula, resulting in an incorrect answer. The correct formula for change in kinetic energy is 6 * h_bar^2 / 2I, taking into account the energy of the emitted photon. This mistake could have been avoided by double checking the formula and units used, as well as considering all sources
  • #1
Guessit
5
0

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:
Physics news on Phys.org
  • #2
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.
 

FAQ: Moment of Inertia of dysprosium-160

What is the Moment of Inertia of dysprosium-160?

The Moment of Inertia of dysprosium-160 is a measure of its resistance to rotational motion. It is a physical property that depends on the distribution of mass around the axis of rotation.

How is the Moment of Inertia of dysprosium-160 calculated?

The Moment of Inertia of dysprosium-160 can be calculated using the formula I = m*r^2, where I is the moment of inertia, m is the mass of the object, and r is the distance from the axis of rotation to the mass. This formula can be applied to different shapes and distributions of mass to calculate the moment of inertia.

Why is the Moment of Inertia of dysprosium-160 important?

The Moment of Inertia of dysprosium-160 is important because it helps us understand how the element will behave when subjected to rotational forces. It is also a crucial factor in many engineering and design applications, such as building structures and machines.

How does the Moment of Inertia of dysprosium-160 compare to other elements?

The Moment of Inertia of dysprosium-160 is different for each element, as it depends on factors such as mass and distribution of mass. However, compared to other rare earth elements, dysprosium-160 has a relatively high moment of inertia due to its larger atomic mass and unique electron structure.

Can the Moment of Inertia of dysprosium-160 change?

Yes, the Moment of Inertia of dysprosium-160 can change depending on the object's shape, mass, and distribution of mass. For example, if the mass of dysprosium-160 is concentrated closer to the axis of rotation, its moment of inertia will be lower compared to when the mass is distributed farther away from the axis. Additionally, the moment of inertia can also change if the object's shape is altered, such as through compression or elongation.

Similar threads

Moment of Inertia: Non Uniform Rod
Replies
1
Views
3K
Find the moment of inertia of a washer
Replies
4
Views
4K
Rod w/ Pivot and Attached Mass Pendulum
Replies
4
Views
2K
What is the moment of inertia I for rotation around r_cm?
Replies
7
Views
1K
Moment of Inertia of Half Ring (Half Circle)
Replies
2
Views
4K
Moment of inertia and torque of a yoyo
Replies
9
Views
5K
Moment Of Inertia Of Non-uniform Rod
Replies
7
Views
5K
Concept of Moment of Inertia and its limits of integration
Replies
4
Views
1K
Moment of Inertia of a Changing System
Replies
5
Views
4K
How to Calculate the Moment of Inertia of a Thin Rod About an Off-Center Axis?
Replies
6
Views
13K

Hot Threads

Recent Insights

Back
Top