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A Geiger counter used in several applications over the course of a typical day produces on the average 100 counts per second. The tube is in the form of a cylinder 5 cm in diameter by 20 cm long and is filled with a mixture of 90% argon and 10% ethanol to a pressure of 0.1 atmosphere. In the Geiger-Muller region, each output count results from the formation of about 1010 ion-electron pairs. How long will it take for one-third of the quenching gas to be used up, thus necessitating replacement of the tube

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danialamin

Answer:

As it is given that

[tex]activity=\lambda= 100\\[/tex]

[tex]Number~of ~counts=100/second\\[/tex]

Using formula

[tex]ln(\frac{N}{N_o})=-\lambda\cdot t\\\\[/tex]

or

[tex]-\frac{ln(\frac{N}{N_o})}{\lambda}= t\\\\[/tex]

where [tex]N=\frac{N_o}{3}[/tex]

[tex]-\frac{ln(\frac{1}{3})}{100}= t\\\\\-\frac{-1.0986}{100}=t\\\\[/tex]

[tex]\frac{1.0986}{100}=t\\1.0986\cdot 10^{-2}seconds=t\\[/tex]

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