A sample F-18 has an initial decay rate 1.5 x 105 /s. How long will it take for

Question

A sample F-18 has an initial decay rate 1.5 x 105 /s. How long will it take for the decay rate to fall 1.0 x 102 /s? ( F-18 has a half-life of 1.83 hrs). Please can you give me like 5th grade details on the calculations? A sample F-18 has an initial decay rate 1.5 x 105 /s. How long will it take for the decay rate to fall 1.0 x 102 /s? ( F-18 has a half-life of 1.83 hrs). Please can you give me like 5th grade details on the calculations? A sample F-18 has an initial decay rate 1.5 x 105 /s. How long will it take for the decay rate to fall 1.0 x 102 /s? ( F-18 has a half-life of 1.83 hrs). Please can you give me like 5th grade details on the calculations?

Explanation / Answer

According to 1st order kinetics
rate constant (k), initial concentration (A0), concentration @ time t (At)

Given that half-life of 1.83 hrs

So t1/2 =0.693/ k

rate constant = 0.693/ 1.83

= 0.379 hr-1

And A0= 1.5 x 10^5 /s

At = 1.0 x 10^2 /s

k*t = ln ( A0/At)

t = (1/0.379 hr-1)*ln (1.5 x 10^5 /1.0 x 10^2)

= (1/0.379 hr-1)*ln 1500

=2.64 * 7.31

= 19.28 hrs

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