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The thickness of lead needed to stop half of the neutrinos in a beam is about 3000lightyears (which you may take as 3.0×1019m).Calculate the fraction of neutrinos which would be stopped by 100m of water assuming that the attenuation coefficients for water and lead are about the same (which they’re not). You may need to use the approximation e^x≈1 x provide x has a small magnitude.
Original post by sa45
The thickness of lead needed to stop half of the neutrinos in a beam is about 3000lightyears (which you may take as 3.0×1019m).....


First, evaluate the attenuation coefficient μ0.

0.5=eμ0×3.0×1019 0.5 = e^{- \mu_0 \times 3.0 × 10^{19}}

Original post by sa45
.....Calculate the fraction of neutrinos which would be stopped by 100m of water assuming that the attenuation coefficients for water and lead are about the same (which they’re not). You may need to use the approximation e^x≈1 + x provide x has a small magnitude.


Make use of the usual attenuation relationship to find the fraction :

I=I0eμ0x I = I_0 e^{- \mu_0 x}

Rearrange and use the approximate exponential form:

II01μ0x \dfrac{I}{I_0} \approx 1 - \mu_0 x

1II0μ0x 1 - \dfrac{I}{I_0} \approx \mu_0 x

1II0 1 - \dfrac{I}{I_0} is the fraction of neutrinos which would be stopped by 100 m of water.
Reply 2
Thank you very much!
Original post by sa45
Thank you very much!


You are welcome. What level of physics are you doing?
Reply 4
Original post by Eimmanuel
You are welcome. What level of physics are you doing?

A2 Level Physics

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