The formula for half-life is:
[tex]A_{final}=A_{initial}(\frac{1}{2})^{\frac{t}{h}}[/tex]
Where A is the amount of iodine-131 initially and after 40 days, t is time, h is half-life of the isotope. Let's plug in our values to the equation:
[tex]A_{final}=20(\frac{1}{2})^{\frac{40}{8}=0.625g[/tex]
Therefore, the patient has 0.625 grams of iodine-131 after 40 days.
Half- life is the time in which the quantity of the radioactive substance remains half of its initial quantity. 0.625 grams of iodine-131 will remains after 40 days.
The formula of half life,
[tex]\bold {N(t) = N_0 (\dfrac 12)^\frac th}[/tex]
Where,
N(t) = quantity of the substance remaining
No = initial quantity of the substance
t = time elapsed
h = half life of the substance
Put the values in the formula,
[tex]\bold {N(t) = 20(\dfrac 12)^\frac {40\ days}{8\ days}}\\\\\bold {N(t) = 20(\dfrac 12)^5}\\\\\bold {N(t) = 0.625\ g}[/tex]
Therefore, 0.625 grams of iodine-131 will remains after 40 days.
To know more about radioactivity,
https://brainly.com/question/13214440
