Mass attenuation problem, protecting the lunar base against radiation?

[carnivalcougar]

Homework Statement

To protect the lunar base against space and sun radiation, astronauts covered it with 4m thick layer of regolith (moon soil). However, they found that they level of radiation was still 50% higher than on the Earth's surface, which they want to match. How many more meters of regolith do they need to add for proper protection?

Homework Equations

I = I˳e-µx

The Attempt at a Solution

I know that they want to reduce the radiation by 1/3, to 2/3 of the current value. However, no half layer value or absorption coefficient is given for regolith.

 

[berkeman]

Homework Statement

To protect the lunar base against space and sun radiation, astronauts covered it with 4m thick layer of regolith (moon soil). However, they found that they level of radiation was still 50% higher than on the Earth's surface, which they want to match. How many more meters of regolith do they need to add for proper protection?

Homework Equations

I = I˳e-µx

The Attempt at a Solution

I know that they want to reduce the radiation by 1/3, to 2/3 of the current value. However, no half layer value or absorption coefficient is given for regolith.

If 4m of soil attenuates to 1.5 times the intensity at the earth, how many meters of soil is needed to attenuate to 1.0 times the intensity at the earth. The attenuation rate is constant, so...

 

[carnivalcougar]

Would this just be 5.333m? if 4m attenuates to 1.5x Earth radiation, then 1/3 more regolith would attenuate to 1x Earth radiation. 4x(1/3) = 1.333 and 4+1.333 = 5.333

 

[berkeman]

Would this just be 5.333m? if 4m attenuates to 1.5x Earth radiation, then 1/3 more regolith would attenuate to 1x Earth radiation. 4x(1/3) = 1.333 and 4+1.333 = 5.333

I'm not following your math, but it doesn't look exponential.

Draw a graph of I versus distance, with the plot having an exponential shape. The initial intensity with no attenuation is Io on the y-axis at distance d=0. The exponential I plot falls to a value of 1.5*Ie at a distance of d=4m. Can you then solve for how much more distance d it takes to have that exponential decay fall to 1.0*Ie?

 

[carnivalcougar]

For this problem, I = I˳e^-µx

I = 1 and I˳ = 1.5
x = 4m + some distance
μ = no idea

They do not give the half value layer λ which is related to μ by μ = ln2/λ

Therefore, I'm not seeing how to solve the problem.

If you start with I = 1.5 , I˳ = original intensity before the regolith (not sure what it would be, it's not given) then x = 4m and μ = unkown. There are still two unknowns in that problem.