Can radiation from nuclear decay be considered a gas? The reason I ask this is because I need to calculate the de Broglie wavelength of a neutron in thermal equilibrium with a nuclear reactor at temperature $500$K. 
The only way I can think to do this is to use the internal energy equation of an ideal gas, namely $$E=\frac32 NK_B T\tag{1}$$ where $N$ is the number of particles, $K_B$ is the Boltzmann constant and $T$ is the thermodynamic temperature.
Since we are only considering $1$ neutron here; $N=1$ and $(1)$ reduces to $$E=\frac32 K_B T\tag{2}$$
The momentum $p$ is given by $$p=\sqrt{2m_n\,E}=\sqrt{3m_n\,K_B\,T}$$ where $m_n$ is the mass of a neutron, so $$\lambda=\frac{h}{p}=\frac{6.63\times 10^{-34}}{\sqrt{3\times 1.675\times10^{-27}\times 1.38\times 10^{-23}\times 500}}\approx1.13\times 10^{-10}\,\text{m}$$ This is actually the correct answer. What I would like to know is whether I can use equation $(1)$ to find the de Broglie wavelength. 
In other words; is it plausible to think of radiation as a gas?

EDIT:
One answer suggests that it is okay to think of radiation as an ideal gas, but my main concern is that this equation $(1)$ is identical to the formula used in the theorem of Equipartition of energy. 
So the question that remains is: Was the internal energy equation $(1)$ a simple coincidence in that it is equal to the formula used in the theorem of equipartition of energy?
Or put in another way; Which theorem is applicable to this situation? 
 A: Yes i think it is correct in thinking of the emitted neutrons as ideal gas molecules since you get $E = \frac{3}{2}NK_BT$ from kinetic theory of gases which has under its number of assumptions, the following two :
1) Molecules dont interact with each other (no attractive or repulsive force; they are neutral to other molecules' presence)
2)They are thought of hard, pointlike spheres(very negligible size) which dont deform on collision (which are perfectly elastic)
These can be clearly applied to a bunch of neutrons inside a reactor.
A: The issue here is one of time scales. The neutrons come off fission events with large and non-thermal energy. They will also either capture or decay before to long.
So there are a range of possibilities between

Neutrons decay or are capture while their energy spectrum is still dominated by the conditions of their creation.

(in which case treating them with equipartition is completely erroneous) through

The neutrons thermalize fast enough and last long enough that the bulk of their existence as a separate species is spent in thermal equilibrium with their surroundings.

(under which conditions the approximation is entirely reasonable).
All of which means we need a way to estimate how long thermalization takes. To do that we ask how neutrons interact with their surroundings and how often that happens.
For the purposes of a BotE calculation we can treat neutron interaction with their surroundings as a contact interaction with nuclei, which gives us a cross-section on order of a few tens of millibarns. (Nucleon radius is about one femtometer and nuclear radius is up to a few times that, so the impact parameter for significant energy transfer is order of $2$–$5 \,\mathrm{fm}$, and cross-sections go by the square of the impact parameter...)
Mean free path is cross-section times number density. In a reactor environment the number density is roughly a few thousand moles per cubic meter. So mean-free path is of order $10^{-4}$–$10^{-3}\,\mathrm{m}$.
At nuclear decay and fission energies neutron speeds are non-relativistic, but still quite fast. Let's use $10^6\,\mathrm{m/s}$.
So the fast neutrons have an initial scattering rate around a billion times per second or a thousand times per microsecond. On average the neutron will lose about half it's energy on each scattering until it reaches energies comparable to thermal environment. That's about 25 scatterings for a $1 \,\mathrm{MeV}$ neutron.
Absorption times in a water environment are tens of microseconds and up, so we can safely treat them as thermal for most of their lifetime.
