Radiation from a point source obeys the Inverse-square law. If the count rate at a distance of 1.0 m from the Geiger counter is 360 counts per minute, what will be its count rate at 3.0 m from the source?

(Ans: 40 counts per min.)



Given Data:

1st distance of source from Giger Counter = r₁ = 1.0 m

1st Count Rate of Giger Counter = I₁ = 360 Counts per min

2nd distance of source from Giger Counter = r₂ = 3.0 m




To Find:

2nd Count Rate of Giger Counter = I₂ = ?


Solution:


Since

I ∝ `\frac {1}{r^2}` or I = `\frac {K}{r^2}` -----(1)

For 1st distance r₁ eqn (1)


I₁ = `\frac {K}{r₁^2}` --------------(2)


For 2nd distance r₂ eqn (1)

I₂ = `\frac {K}{r₂^2}` --------------(3)

Now dividing eqn (2) by (3)

`\frac {I₂}{I₁}` = `\frac {K}{r₂^2}/frac {K}{r₁^2}`

or

I₂ = I₁`\frac {r₁^2}{r₂^2}`

by putting values

I₂ = 360 counts/min ｘ`\frac {(1.0 m)^2}{(3.0 m)^2}`

I₂ = 360 counts/min ｘ`\frac {1}{9}`

I₂ = 40 counts/min ----------------Ans.




************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.