Question

Radiation is being emitted from a source of uranium in the form of neutrons. You want to move farther away from the source to protect yourself (obviously); however, you know radiation flux (particles/area) is inversely proportional to the square of the distance you are from the source. If you are 10 feet away right now, how many feet should you run away to reduce the flux you are exposed to by a factor of 4?

Answer 1

\[I(r)\propto r^{-2}\]

Answer 2

@UnkleRhaukus I'm unfamiliar with what you wrote. I haven't quite learned that?

Answer 3

Not sure if it is the right way to do it.
Flux = k/ (x^2) , where x is the distance from the source.
Flux (10^2) = [(1/4) Flux] (x^2)
100 = 1/4 (x^2)
x= 20

Distance required = 20 -10 = 10 ft

Answer 4

If X is the radiation flux you get at 10 feet:
\[X = \frac{\alpha}{10^{2}}\]
Y is the distance you want to run away to reduce the flux by 4:
\[\frac{X}{4} = \frac{\alpha}{(10+Y)^{2}}\]
Solve for X:
\[X = \frac{4\alpha}{(10+Y)^{2}}\]
X=X, so:
\[\frac{\alpha}{10^{2}} = \frac{4\alpha}{(10+Y)^{2}}\]
\[\frac{1}{10^{2}} = \frac{4}{(10+Y)^{2}}\]
\[(10+Y)^{2} = 4*10^{2}\]
\[(10+Y)^{2} = 2^{2}*10^{2} = (2*10)^{2} = 20^{2}\]
10+Y = 20
Y=10

Answer 5

i am getting 5 feet. you should move away 5 feet to reduce the flux by a factor of 4

Answer 6

The explanation says that 10 ft is the answer, but I'm not sure what you did? The answer they gave was similar, but I don't know what was going on. They said:
\[F(10)^{2} = \frac F4(d + 10)^{2} = d + 10 = 20 \rightarrow d = 10\]
Alright @Wired I think I see what you did :) I'm still a bit curious with the other method.

Answer 7

lets say, flux at the current distance from source : \[ \frac{k}{10^2}\]

we need to find at what distance "r" flux becomes 1/4th :
so,

\[\frac{k}{10^2}\ = \frac{k}{4r^2} \]

solve for r
r=5 feet

Answer 8

@ganeshie8 I think you divided by 4 on the wrong side.

Answer 9

Let F = flux . x = distance away from the source.

''radiation flux (particles/area) is inversely proportional to the square of the distance you are from the source.''


Flux = k/ (x^2) , where k is the variation constant.
F (x^2) = k

New flux = (1/4 )F

F (10^2) = [(1/4) F] (x^2)
100 = 1/4 (x^2)
x= 20

Answer 10

Since the question asks how many ft you need to move, and you're originally 10 ft from the source. So,
distance you need to move = 20-10 = 10ft

Answer 11

I actually have to go now, but thanks everyone! @ganeshie8 the answer that they gave me was 10. Thanks @Wired &@RolyPoly for the great explanations!

Answer 12

If there's radiation, RUN FOR IT! :) Glad to help @Calcmathlete

Answer 13

Run for it o.o?
Run away from it!!!

Answer 14

lol