# Finding the number of particles scattered by a certain angle

I'm trying to do the problem below, but it seems like there is incomplete information.

PROBLEM STATEMENT: In a scattering experiment, $10^6$ $\alpha$ particles are scattered at an angle of $4^{\circ}$. Find the number of $\alpha$ particles scattered at an angle of 6$^{\circ}$.

The reason it seems incomplete is because the number of particles scattered at an angle of $6^{\circ}$ would be dependent on the "intensity profile" of the incident beam, right?

By intensity profile, I mean the following (see figure for reference): Imagine that there are no particles other than those that are coming in at distance $s$. In such a case, $\it all$ particles would be deflected by a certain amount, say $\Theta$, and no particles would be deflected by any other amount. Therefore, it seems like the number of particles deflected by any given angle is a direct function of the profile of incident beam, which is not given in the problem statement. To put things another way, the problem statement gives me the information that $10^6$ particles were located at distance $s$, assuming that $\Theta = 4^{\circ}$. It does not tell me how many particles were located at any distance other than $s$. I am assuming a classical picture, which is therefore completely deterministic.

The nuclei of the target can be assumed to be uniformly distributed and beam variation happen on a much (much!) larger spacial scale2 so the impact parameters ($s$) are effectively uniformly random as well.
2 At JLAB we could measure beam intensity variations at the $10^{-5}$ meter level, but that is still huge compare to inter-atomic spacing. In Rutherford's experiment it would have depended on the size of the collimator.