Radioactive activity

Содержание и основные понятия

Unstable kernels break up spontaneously with the release of particles or electromagnetic radiation; for a large ensemble, the number of unsprayed kernels is reduced by the exponent.
GEF · Grade 9
PIF · Baseline
Interactive model
Radioactiveity
Half-life
Activity
Dose
01
The physical picture
What happens and what boundaries the model has.
Main message
Unstable kernels break up spontaneously with the release of particles or electromagnetic radiation; for a large ensemble, the number of unsprayed kernels is reduced by the exponent.
Alpha, beta and gamma radiation differ in nature and penetration.
The half-life is independent of the sample ' s age and almost independent of external conditions.
The protection is chosen by type of radiation, time, distance and screen material.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
N
=
N
0
2
−
t
/
T
1
/
2
N=N_0\,2^{-t/T_{1/2}}
N
=
N
0
​
2
−
t
/
T
1/2
​
law of dissolution
A
=
λ
N
A=\lambda N
A
=
λ
N
Activity
Review of the situation
Three half-lives leave 1/8 of the original number of radioactive kernels.
04
Links and application
In the real world
Three half-lives leave 1/8 of the original number of radioactive kernels.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Radioactivity" through the model, not just the formula.
Outcome 2
Clear and correct use of terms: radioactivity, half-life, activity.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Radioactiveity
The spontaneous transformation of unstable atomic nuclei.
Half-life
The time over which, on average, half of the large initial number of radioactive kernels is dissolved.
Activity
Average number of radioactive breakdowns per unit of time.
Dose
The energy measure of the ionizing radiation transmitted to the substance; the specific dose type sets the method of rationing.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
N
=
N
0
2
−
t
/
T
1
/
2
N=N_0\,2^{-t/T_{1/2}}
N
=
N
0
​
2
−
t
/
T
1/2
​
empirical law
The law of dissolution.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
N
(
T
1
/
2
)
=
N
0
2
N(T_{1/2})=\frac{N_0}{2}
N
(
T
1/2
​
)
=
2
N
0
​
​
The half-life is set experimentally as the time over which, in large aggregate, half of the unsplit kernels remain.
N
(
n
T
1
/
2
)
=
N
0
(
1
2
)
n
N(nT_{1/2})=N_0\left(\frac12\right)^n
N
(
n
T
1/2
​
)
=
N
0
​
(
2
1
​
)
n
The independence of breakups means that in each next period half of the remaining kernels are dissolved again.
n
=
t
T
1
/
2
⇒
N
=
N
0
2
−
t
/
T
1
/
2
n=\frac{t}{T_{1/2}}\Rightarrow N=N_0\,2^{-t/T_{1/2}}
n
=
T
1/2
​
t
​
⇒
N
=
N
0
​
2
−
t
/
T
1/2
​
The transition to arbitrary time gives an exponential law, established by statistical observations of radioactivity, rather than proven for a single kernel.
Conditions:
A large number of identical unstable kernels, constant probability of decay and constant external conditions; the formula sets the expected average N.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
A
=
λ
N
A=\lambda N
A
=
λ
N
model effect
Activation.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
A
≡
−
d
N
d
t
A\equiv-\frac{dN}{dt}
A
≡
−
d
t
d
N
​
Activity is introduced as the average number of break-ups per unit of time; minus the decrease of N.
d
N
d
t
=
−
λ
N
\frac{dN}{dt}=-\lambda N
d
t
d
N
​
=
−
λ
N
For radioactive decay, the probability of decay in short periods is constant, so the rate of decay is proportional to the number of remaining kernels.
A
=
−
d
N
d
t
=
λ
N
A=-\frac{dN}{dt}=\lambda N
A
=
−
d
t
d
N
​
=
λ
N
The replacement of the law of decay links the activity to the permanent decay and the current number of kernels.
Conditions:
A homogeneous radioactive nuclide with constant , N large enough for statistical averaging, A is measured in bakerels.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
The key condition of this topic is that Alpha, beta and gamma radiation differ in nature and penetration.
How to Check the Mind
The half-life is independent of the sample ' s age and is almost independent of external conditions. Then check the units, vector direction and behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Radioactive activity
Unstable kernels break up spontaneously with the release of particles or electromagnetic radiation; for a large ensemble, the number of unsprayed kernels is reduced by the exponent.
Alpha, beta and gamma radiation differ in nature and penetration.
The half-life is independent of the sample ' s age and almost independent of external conditions.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.