A certain radioactive isotope placed near a Geiger counter registers 160 counts per minute. Eight hours later, the counter registers 10 counts per minute. What is the half-life of the isotope

The half-life of the isotope is 2 hours

Explanation:

The Geiger counter  is a device that is used for the detection and measurement of all types of radiation( that is alpha, beta and gamma radiation).

Initially, the Geiger counter also known as the Geiger Muller tube registers 160 counts per minutes when placed near a radioactive isotope. After eight hours, the counter registers 10 counts per minute, this reduced number of counts means that n half lives has elapsed.

10 counts per minute = 1/16 of 160 counts per minutes.

Therefore 1/16 = 1/2⁴, comparing 1/2⁴ with where n is the number of elapsed half lives, n = 4. This means that 4 half lives has elapsed after 8 hours.

Therefore one half life of the isotope = 8/4 = 2 hours.

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