Final answer:
To calculate the remaining mass of Rn-222 after 19.1 days, the half-life decay formula is used. After 19.1 days, 5 mg of the original 160 mg sample of Rn-222 would remain.
Step-by-step explanation:
The question asks to determine the remaining mass of Rn-222 after 19.1 days from an original sample of 160 mg, given the half-life of Rn-222 is 3.823 days. To solve this, we'll use the half-life decay formula:
N(t) = N0 * (1/2)^(t/T)1/2
- N(t) is the remaining quantity of the substance after time t,
- N0 is the initial quantity,
- t is the elapsed time,
- T1/2 is the half-life of the substance.
Let's calculate it:
N(t) = 160 mg * (1/2)^(19.1 days / 3.823 days)
= 160 mg * (1/2)^(5)
= 160 mg / 2^5
= 160 mg / 32
= 5 mg
Therefore, after 19.1 days, 5 mg of the original Rn-222 would remain.