Francium-233 has a half-life of 22 minutes. A Geigor counter gives a reading of 58 counts per minute (cpm) from a sample of francium-233.What will the reading be 22 minutes later?You can ignore background radiation

The reading of the Geiger counter, 22 minutes later = 29 counts per minute (cpm)

Explanation:

Half life is defined as the time taken for the amount ( or activity) of a substance to reduce to half its original value.

As stated in the question, the half life of Francium-233 is 22 minutes, . This means that it takes 22 minutes for the activity of Francium-233 to reduce to half of its original value.

The original activity of Francium-233 =  58 counts per minute (cpm)

By the end of 22 minutes, the activity measured by the counter would have halved.

Activity of Francium-233 after 22 minutes = 58/2

Activity of Francium-233 after 22 minutes = 29 counts per minute (cpm)

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west