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Zeitdauer für Helium aus Radonzerfall

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Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

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Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/zeitdauer-fur-helium-aus-radonzerfall/

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The following quantities appear in the problem: Zeit \(t\) / Masse \(m\) / molare Masse \(M\) / Stoffmenge \(n\) / Zerfallskonstante \(\lambda\) / Anzahl \(N\) /

The following formulas must be used to solve the exercise: \(m = nM \quad \) \(N_t = N_0 \cdot \text{e}^{-\lambda t} \quad \)

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Exercise:
Das radioaktive Nuklid isotopeRn zerfällt mit der Halbwertszeit .d nach der Kernreaktionsformel isotopeRn rightarrow isotopePo + isotopeHe. Wie lange dauert es bis aus mg Radon- nach dieser Reaktion microgram Helium entstanden sind?

Solution:
Die mg Radon entsprechen n_ fracmM .mol N_ n N_A numpr.e Radon-Atomen. Die microgram Helium entsprechen Delta n fracmM .mol Delta N n N_A numpr.e Helium-Atomen. Diese sollen aus dem Zerfall von anfänglich N_ Radon-Kernen entstehen. Nach Ablauf der Zeit t liegen noch N Radon-Kerne vor; d.h. N_-N Radon-Kerne sind zerfallen und aus jedem dieser Zerfälle ist ein Helium-Kern entstanden nebst einem Polonium-Kern. Daher gilt folges: N_-N &mustbe Delta N N_-N_ texte^-lambda t Delta N N_ -texte^-lambda t Delta N t -fraclambda lnleft-fracDelta NN_right .es .h

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Tags	kernphysik, kernreaktion, physik, radioaktivität, radon, zerfall, zerfallsgesetz, zerfallsgleichung
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Difficulty	(3, default)
Points	4 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
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