Answer:
The time take is [tex]t = 1.3964 \ days[/tex]
Explanation:
From the question we are told that
The decay constant is [tex]\lambda = 0.16[/tex]
The percentage fall is [tex]c = 0.80[/tex]
The equation for radioactive decay is mathematically represented as
[tex]N(t) = N_o * e^{- \lambda t }[/tex]
Where is [tex]N(t)[/tex] is the new amount of the new the isotope while [tex]N_o[/tex] is the original
At initial [tex]N_o = 100[/tex]% = 1
At [tex]N(t ) = 80[/tex]% = 0.80
[tex]0.80 = 1 * e^{- 0.16 t }[/tex]
=> [tex]-0.223 = -0.16 t[/tex]
=> [tex]t = 1.3964 \ days[/tex]
