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If the intensity of an X-ray becomes I/3 from I after travelling 3.5 cm inside a target, then it's intensity after travelling next 7 cm will be 1) I/6 2) I/12 3) I/9 4) I/27 Pls answer without using natural log

If the intensity of an X-ray becomes I/3 from I after travelling 3.5 cm inside a target, then it's intensity after travelling next 7 cm will be 
1) I/6 
2) I/12
3) I/9
4) I/27
Pls answer without using natural log 

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
Intensity of X rays  after traversing a distance x is given by

I = I0e−μx,

where I0 is the initial intensity of X rays and μ the absorption coefficient.

From the data given, we can write
I0/3 = I0e−3.5μ
⇒  1/3 = e−3.5μ
3 = e3.5μ
ln 3 = 3.5 μ
1.0986 = 3.5 μ
⇒  μ = 0.313885 cm−1
When x = 3.5 cm + 7 cm = 10.5 cm, the intensity is
I = I0e−μx
  = I0e−0.313885x 10.5,
  =  I0e−3.2958,
  =.0370 I0

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