Neutron Attenuation 1st order ODE Interpertation

[terryphi]

Hi,

I'm having some trouble interpreting an equation. In Lamarsh's Introduction to Nuclear Engineering.

The formulae for neutron attenuation is:

$$I(x) = I_{0} exp(-\Sigma_{t} x$$ I am given the formulae
$$\frac{-dI}{I(x)} = \Sigma_{t} dx$$

This formulae has been described as "the probability of a neutron to have an intereraction between x and x+dx"

However, I do not understand where this interpertation arises from. I mean dividing dI/I(x) just doesn't have any meaning to me.

I understand the math, but the formulae isn't apparent to me on any kind of intutitve level.

 

[QuantumPion]

Hi,

I'm having some trouble interpreting an equation. In Lamarsh's Introduction to Nuclear Engineering.

The formulae for neutron attenuation is:

$$I(x) = I_{0} exp(-\Sigma_{t} x$$ I am given the formulae
$$\frac{-dI}{I(x)} = \Sigma_{t} dx$$

This formulae has been described as "the probability of a neutron to have an intereraction between x and x+dx"

However, I do not understand where this interpertation arises from. I mean dividing dI/I(x) just doesn't have any meaning to me.

I understand the math, but the formulae isn't apparent to me on any kind of intutitve level.

Re-arrange terms like so:

$$-\frac{dI}{dx} = \Sigma_{t} I(x)$$

and you get: the rate of change of the intensity of the beam with respect to x equals the intensity of the beam at x times the interaction rate. This is the simplest type of differential equation, where the value of some quantity depends on its own rate of change times a constant.