Fluence of Neutrons from Isotropic Pt Source for Train Passengers

[Aksman]

An isotropic point source of neutrons emits 10E8 fast neutrons per second. It is 3m horizontally away from a train track. A train goes by at 60 miles per hour. Ignoring scattering and attenuation, what is the fluence (i.e. neutrons per meter square) of neutrons that would strike a pasenger at the same level with the source? These are the details of a problem, and I feel that it is simpler that I believe it to be, but I cannot take the first step. What would be some assumptions if any that I should make, in order to go about solving the problem?

 

[malawi_glenn]

This is a problem from the book of Attix.

No assumptions, just calculate it. Start with doing a sketch. Assume train starts from +infinity on y-axis and ends in -infinity. Try to find a realation between its position on y-axis and the angle and radial distance to the source, and then convert into fluence (you know the position, and velocity, find the trains temporal distribution i.e the angle and radial distance as a function of time)

 

[Aksman]

What do you mean by the train's temporal distribution...that is where I get stuck...I don't know how to use the velocity.

 

[malawi_glenn]

z = v*t

 

[malawi_glenn]

do a try and I'll help you, I have done this problem myself in school :-)

 

[granpa]

if the train is infinitely long then how many neutrons strike it every second?

there's a fairly simple solution (for simplicity just assume the train is one meter high)how long would it take to move one meter at 60 mph?

 

[malawi_glenn]

Are you making progress aksman?

granpa: have you done this exercise yourself and got the correct answer? (3.11E5 neutrons/m^2)

 

[granpa]

a 2 meter high train at 3 meters makes an angle of 60 degrees so 1/6th the neutrons should strike it. at a mile (1.61 km) a minute one covers 0.5 meters in 0.5*60/1610 seconds. which equals 0.01863354037267080745.

0.01863354037267080745* 1/6 * 1E9=3.10559006211180124e6

 

[malawi_glenn]

You should not assue that the train is 2m high.

One should use fluence and flux concepts here, which is covered in the first chapter in the book of Attix (where this problem comes from)

There is a quite easy and elegant way to do this problem, which uses the concepts covered in the book, but we must wait til the OP show attempt to solution. Read and follow forum rules, this also applies to HW-helpers.

 

[granpa]

You should not assue that the train is 2m high.
.

a person is 2 meters high. plus it makes no difference. the question was about a 1 square meter. I used 2 meters because it was convenient then canceled it out with the 0.5 meter in the second part.

 

[granpa]

actually, I guess it makes an angle of 36 degrees. so only 1/10th the neutrons strike the train.

 

[Redbelly98]

I think the goal is for Alksman to think about and solve the problem now that he has gotten a hint or two, since it is his school homework.

 

[granpa]

agreed

 

[malawi_glenn]

actually, I guess it makes an angle of 36 degrees. so only 1/10th the neutrons strike the train.

yes the angle is 36degree with your configuration, and you have never used the concept of flux or fluence.

 

[albphys08]

hi everyone - new member here. i am also working on this problem in class. i know i need to be using solid angle here and I'm getting confused how to apply it. I've looked at the train's velocity and did some dimensional analysis to determine it's going 26.82 m/sec. i know that i need to be determining the fluence and i think that the per unit area part of the equation will be impacted by the solid angle piece... i also think that the inverse square law is going to come into play here because obviously the farther away the train is the smaller the impact of the neutrons. any other hints or suggestions?

 

[granpa]

is the one square meter always facing the neutron source?

 

[albphys08]

does that matter if it's always facing the neutron source? I'm not sure i understand your reply... sorry!

 

[granpa]

does what matter?

 

[albphys08]

you said "is the one square meter always facing the neutron source?". i don't understand how that has bearing on the fluence.

 

[malawi_glenn]

All you need is the connection betweem flux and fluence and how to relate the radial distance to the source as a function of time.

 

[granpa]

http://en.wikipedia.org/wiki/Fluence

In physics, fluence or integrated flux is defined as the number of particles that intersect a unit area . Its units are m–2 (number of particles per meter squared).

 

[kmoh111]

Hello all, new member here also. Hopefully this thread is still active. I am working this problem as well. Based on the prior posts, here is how I am approaching the problem - but I'm still having trouble getting the answer in Attix (3.11e5).

We know that fluence is the integral of flux density over time. We can start with the differential flux density dphi = (S/4*pi* R^2) dz.

S is the intensity of the source 10e8.
R is the radial distance. We know that R^2 = z^2 + h^2.
h is a constant and is the distance from the train platform to the track = 3m.
dz = vdt.

Here is where I am having trouble. What are my integral limits? Zero to infinity?

Once I represent R and dz in terms of t and dt, I get an integral for (1/[t^2 + a^2]; where a is a constant and is equal to h^2/v^2. When I look up this integral in a table the result is:

[1/a arctan (t/a)].

When I take the limits from zero to infinity, the result is 1/a * pi/2 ---- which I multiply by the coefficient outside the integral S/4piv. Still, I don't get then answer in Attix.

Where did I go wrong?

 

[malawi_glenn]

You shold to -infinity to + infinity when integrating the time, since the most natural choice is to have t = 0 when train is perpendicular to the source.