Stoffmenge von radioaktiver Probe
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
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
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
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
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Zeit \(t\) / Aktivität \(A\) / Stoffmenge \(n\) / Halbwertszeit \(T\) / Zerfallskonstante \(\lambda\) / Anzahl \(N\) /
The following formulas must be used to solve the exercise:
\(A = \lambda \cdot N \quad \) \(T = \dfrac{\ln 2}{\lambda} \quad \) \(\overline N = A t \quad \) \(P(k) = \frac{\mu^k}{k!} \cdot \text{e}^{-\mu} \quad \) \(N = n \cdot N_{\rm A} \quad \)
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Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Die Wahrscheinlichkeit dass in den nächsten t in einer Cäsium--Probe mindestens ein Zerfallsereignis stattfindet beträgt n. Wie viel Stoffmenge isotopeCs Halbwertszeit T befindet sich in der vorliegen Probe?
Solution:
Die Anzahl Ereignisse bzw. Zerfälle in einer radioaktiven Probe in einem festen Zeitervall ist poisson-verteilt. Um auf die mittlere Ereignisrate lambda in der Mathematik bzw. overline N in diesem Themengebiet schliessen zu können muss die Wahrscheinlichkeit für m bekannt sein denn dann gilt: Pmlambda fraclambda^m texte^-lambdam! Poverline N fracoverline N^ texte^-overline N! texte^-overline N Poverline N texte^-lambda overline N -lnPoverline N -ln-nC lam Daraus kann nun die Aktivität der Probe bestimmt werden: A fracoverline Nt fraclamtC AP Zusammen mit der Zerfallskonstanten lambdafracln T findet man: N fracAlambda fracA Tln Ns n fracNsscNA fracA TsscNA ln ns
Die Wahrscheinlichkeit dass in den nächsten t in einer Cäsium--Probe mindestens ein Zerfallsereignis stattfindet beträgt n. Wie viel Stoffmenge isotopeCs Halbwertszeit T befindet sich in der vorliegen Probe?
Solution:
Die Anzahl Ereignisse bzw. Zerfälle in einer radioaktiven Probe in einem festen Zeitervall ist poisson-verteilt. Um auf die mittlere Ereignisrate lambda in der Mathematik bzw. overline N in diesem Themengebiet schliessen zu können muss die Wahrscheinlichkeit für m bekannt sein denn dann gilt: Pmlambda fraclambda^m texte^-lambdam! Poverline N fracoverline N^ texte^-overline N! texte^-overline N Poverline N texte^-lambda overline N -lnPoverline N -ln-nC lam Daraus kann nun die Aktivität der Probe bestimmt werden: A fracoverline Nt fraclamtC AP Zusammen mit der Zerfallskonstanten lambdafracln T findet man: N fracAlambda fracA Tln Ns n fracNsscNA fracA TsscNA ln ns
Meta Information
Exercise:
Die Wahrscheinlichkeit dass in den nächsten t in einer Cäsium--Probe mindestens ein Zerfallsereignis stattfindet beträgt n. Wie viel Stoffmenge isotopeCs Halbwertszeit T befindet sich in der vorliegen Probe?
Solution:
Die Anzahl Ereignisse bzw. Zerfälle in einer radioaktiven Probe in einem festen Zeitervall ist poisson-verteilt. Um auf die mittlere Ereignisrate lambda in der Mathematik bzw. overline N in diesem Themengebiet schliessen zu können muss die Wahrscheinlichkeit für m bekannt sein denn dann gilt: Pmlambda fraclambda^m texte^-lambdam! Poverline N fracoverline N^ texte^-overline N! texte^-overline N Poverline N texte^-lambda overline N -lnPoverline N -ln-nC lam Daraus kann nun die Aktivität der Probe bestimmt werden: A fracoverline Nt fraclamtC AP Zusammen mit der Zerfallskonstanten lambdafracln T findet man: N fracAlambda fracA Tln Ns n fracNsscNA fracA TsscNA ln ns
Die Wahrscheinlichkeit dass in den nächsten t in einer Cäsium--Probe mindestens ein Zerfallsereignis stattfindet beträgt n. Wie viel Stoffmenge isotopeCs Halbwertszeit T befindet sich in der vorliegen Probe?
Solution:
Die Anzahl Ereignisse bzw. Zerfälle in einer radioaktiven Probe in einem festen Zeitervall ist poisson-verteilt. Um auf die mittlere Ereignisrate lambda in der Mathematik bzw. overline N in diesem Themengebiet schliessen zu können muss die Wahrscheinlichkeit für m bekannt sein denn dann gilt: Pmlambda fraclambda^m texte^-lambdam! Poverline N fracoverline N^ texte^-overline N! texte^-overline N Poverline N texte^-lambda overline N -lnPoverline N -ln-nC lam Daraus kann nun die Aktivität der Probe bestimmt werden: A fracoverline Nt fraclamtC AP Zusammen mit der Zerfallskonstanten lambdafracln T findet man: N fracAlambda fracA Tln Ns n fracNsscNA fracA TsscNA ln ns
Contained in these collections
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Poisson-Verteilung bei Radioaktivität by TeXercises
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| Title | Matched on |
|---|---|
| Aktivität von Mangan | formula |
| Masse von Hafnium-Isotopen | formula |
| Anfangsaktivität von Polonium | formula |
| Mittlere Ereignisrate von radioaktiver Probe | tagsformula |
| Aktivität von Uran-Mineral nach bestimmter Zeit | formula |
Similar exercises (8)
| Title | Matched on |
|---|---|
| Aktivität von Mangan | formula |
| Masse von Hafnium-Isotopen | formula |
| Anfangsaktivität von Polonium | formula |
| Mittlere Ereignisrate von radioaktiver Probe | tagsformula |
| Aktivität von Uran-Mineral nach bestimmter Zeit | formula |
| Aktivität von Cäsium | formula |
| Anzahl Technetium-Isotope | formula |
| Wahrscheinlichkeit einer bestimmten Zerfallszahl | tags |