Calculating Half-Life: When 131I Will Remain in Body at 1% Level

[HugoPang1]

Homework Statement

When iodine is ingested by humans they eliminate it such that on half of the body's iodine content is execreted every 4.0 days. Radioactive ¹³¹I with a physical half-life of 8.1 days is administered to a patient. When will only 1% of the isotope remain in the patient's body?

Homework Equations

1/T_1/2, e = 1/T_1/2,p + 1/T_1/2,b

The Attempt at a Solution

I got the rest of the equation but I don't know how people got T_1/2,e = 2.7 d

Help please!

 

[PeterO]

Homework Statement

When iodine is ingested by humans they eliminate it such that on half of the body's iodine content is execreted every 4.0 days. Radioactive ¹³¹I with a physical half-life of 8.1 days is administered to a patient. When will only 1% of the isotope remain in the patient's body?

Homework Equations

1/T_1/2, e = 1/T_1/2,p + 1/T_1/2,b

The Attempt at a Solution

I got the rest of the equation but I don't know how people got T_1/2,e = 2.7 d

Help please!

It looks like simple arithmetic??

1/T_1/2, e = 1/T_1/2,p + 1/T_1/2,b

→

1/T_1/2, e = 1/4 + 1/8.1

1/T_1/2, e = 0.37345679

→

T_1/2, e = 2.67768595 better known as 2.7d

 

[HugoPang1]

Ah I was thinking so much, I overlooked it. Thank you though!