Question

prepare models using the concept of differential equation for radiocarbon decay​

Answer 1

Answer:

Step-by-step explanation:

Modeling with first order equations (Sect. 1.5).

I Radioactive decay.

I Carbon-14 dating.

I Salt in a water tank.

I The experimental device.

I The main equations.

I Analysis of the mathematical model.

I Predictions for particular situations.

Radioactive decay

Remarks:

(a) Radioactive substances randomly emit protons, electors,

radiation, and they are transformed in another substance.

(b) It can be seen that the time rate of change of the amount N

of a radioactive substances is proportional to the negative

amount of radioactive substance.

N

0

(t) = −a N(t), N(0) = N0, a > 0.

(c) The integrating factor method implies N(t) = N0 e

−at

.

(d) The half-life is the time τ needed to get N(τ ) = N0/2.

N0 e

−aτ =

N0

2

⇒ −aτ = ln1

2

⇒ τ =

ln(2)

a

.

(e) Using the half-life, we get N(t) = N0 2

−t/τ

.