Homework SourseRandon222222 86 Rnis a radioactive gas with a halflife of 38
Randon-222(222 86 Rn)is a radioactive gas with a half-life of 3.82 days. A gas sample contains 4.0 x 108 radon atoms initially. Estimate how many radon atoms will remain after 12 days. Estimate how many radon nuclei will have decayed by this time.
Solution
Given
Half ife of the radioactivity gas, t1/2 = 3.82 days = 330048 s
Number of atoms initially , No = 4.0 *10^8 atoms
Time taken , t = 12 days = 1036800 s
a) Since t1/2 = 0.693 /
= 0.693 / (330048 s) = 2.099 *10^-6 s-1 is the decay constant
By radioactive decay law
N = No e-t
= ( 4.0 *10^8 atoms) e- (2.099 *10^-6 s-1)(1036800 s)
N = ( 4.0 *10^8 atoms)(0.1135)
N = 4.54 *10^7 atoms ˜ 5 *10^7 atoms
b) Number of atoms decayed , N \' = No - N
= ( 4.0 *10^8 atoms) -(5 *10^7 atoms)
N \' = 3.5 *10^8 atoms
N = 4.54 *10^7 atoms ˜ 5 *10^7 atoms
b) Number of atoms decayed , N \' = No - N
= ( 4.0 *10^8 atoms) -(5 *10^7 atoms)
N \' = 3.5 *10^8 atoms
