Fehlerrechnung für Zerfallsgesetz
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:
The following formulas must be used to solve the exercise:
\(\epsilon_f(a,b) \lesssim \left| \frac{\partial f}{\partial x}(a_0, b_0) \right| \Delta x + \left| \frac{\partial f}{\partial y}(a_0, b_0) \right| \Delta y \quad \)
No explanation / solution video to this exercise has yet been created.
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Die Zerfallskonstante von Kohlenstoff- beträgt tlO. Wie viele isotopeC-Kerne hat man nach Ablauf von ttO noch falls man mit tNzO startet?
Solution:
SolQtyNtNzX*exp-lX*tX SolQtyntNtX/ncNAnmol Nach Ablauf der genannten Zeit liegen noch Nt N_ texte^-lambda t Nz texte^-l t Nt nt nt Kerne vor. Der Fehler in der Berechnung ist: SolQtyfNexp-lX*tX*DNzX SolQtyfltX*NzX*exp-lX*tX*DlX SolQtyftlX*NzX*exp-lX*tX*DtX SolQtyDNfNX+flX+ftX SolQtyDnDNX/ncNAnmol Delta N left|fracpartial Npartial N_right| Delta N_ + left|fracpartial Npartial lambdaright| Delta lambda + left|fracpartial Npartial tright| Delta t texte^-lambda t Delta N_ + t N_ texte^-lambda t Deltalambda + lambda N_ texte^-lambda t Delta t fN + fl + ft DN Delta n Dn
Die Zerfallskonstante von Kohlenstoff- beträgt tlO. Wie viele isotopeC-Kerne hat man nach Ablauf von ttO noch falls man mit tNzO startet?
Solution:
SolQtyNtNzX*exp-lX*tX SolQtyntNtX/ncNAnmol Nach Ablauf der genannten Zeit liegen noch Nt N_ texte^-lambda t Nz texte^-l t Nt nt nt Kerne vor. Der Fehler in der Berechnung ist: SolQtyfNexp-lX*tX*DNzX SolQtyfltX*NzX*exp-lX*tX*DlX SolQtyftlX*NzX*exp-lX*tX*DtX SolQtyDNfNX+flX+ftX SolQtyDnDNX/ncNAnmol Delta N left|fracpartial Npartial N_right| Delta N_ + left|fracpartial Npartial lambdaright| Delta lambda + left|fracpartial Npartial tright| Delta t texte^-lambda t Delta N_ + t N_ texte^-lambda t Deltalambda + lambda N_ texte^-lambda t Delta t fN + fl + ft DN Delta n Dn
Meta Information
Exercise:
Die Zerfallskonstante von Kohlenstoff- beträgt tlO. Wie viele isotopeC-Kerne hat man nach Ablauf von ttO noch falls man mit tNzO startet?
Solution:
SolQtyNtNzX*exp-lX*tX SolQtyntNtX/ncNAnmol Nach Ablauf der genannten Zeit liegen noch Nt N_ texte^-lambda t Nz texte^-l t Nt nt nt Kerne vor. Der Fehler in der Berechnung ist: SolQtyfNexp-lX*tX*DNzX SolQtyfltX*NzX*exp-lX*tX*DlX SolQtyftlX*NzX*exp-lX*tX*DtX SolQtyDNfNX+flX+ftX SolQtyDnDNX/ncNAnmol Delta N left|fracpartial Npartial N_right| Delta N_ + left|fracpartial Npartial lambdaright| Delta lambda + left|fracpartial Npartial tright| Delta t texte^-lambda t Delta N_ + t N_ texte^-lambda t Deltalambda + lambda N_ texte^-lambda t Delta t fN + fl + ft DN Delta n Dn
Die Zerfallskonstante von Kohlenstoff- beträgt tlO. Wie viele isotopeC-Kerne hat man nach Ablauf von ttO noch falls man mit tNzO startet?
Solution:
SolQtyNtNzX*exp-lX*tX SolQtyntNtX/ncNAnmol Nach Ablauf der genannten Zeit liegen noch Nt N_ texte^-lambda t Nz texte^-l t Nt nt nt Kerne vor. Der Fehler in der Berechnung ist: SolQtyfNexp-lX*tX*DNzX SolQtyfltX*NzX*exp-lX*tX*DlX SolQtyftlX*NzX*exp-lX*tX*DtX SolQtyDNfNX+flX+ftX SolQtyDnDNX/ncNAnmol Delta N left|fracpartial Npartial N_right| Delta N_ + left|fracpartial Npartial lambdaright| Delta lambda + left|fracpartial Npartial tright| Delta t texte^-lambda t Delta N_ + t N_ texte^-lambda t Deltalambda + lambda N_ texte^-lambda t Delta t fN + fl + ft DN Delta n Dn
Contained in these collections:
-
Fehlerrechnung by uz
Asked Quantity:
Anzahl \(N\)
in
Anzahl \(\rm 1\)
Physical Quantity
Unit
Anzahl (\(\rm 1\))
Base?
SI?
Metric?
Coherent?
Imperial?
\(\rm1.59\cdot 10^{20}\,\): Enigma
\(\rm4.3\cdot 10^{19}\,\): Rubiks Cube
\(\rm18\cdot 10^{18}\,\): Schach-/Weizenkorn-Legende
\(\rm8.1\cdot 10^{67}\,\): 52er-Karten-Set
\(\rm1\cdot 10^{49}\,\): Atome der Erde

