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Anna11
2 days ago
6

131i has a half-life of 8.04 days. assuming you start with a 1.53 mg sample of 131i, how many mg will remain after 13.0 days ___

_______?
a.0.835
b.0.268
c.0.422
d.0.440
e.0.499
Chemistry
1 answer:
lions [2.7K]2 days ago
8 0
In solving this problem, we need to apply the half-life and radioactive decay formulas.

The half-life formula is:
t1/2 = ln 2 / λ

where t1/2 represents half-life and λ symbolizes the radioactive decay constant.
t1/2 = 8.04 days

Thus,
8.04 days = ln 2 / λ
λ = ln 2 / 8.04 days

The radioactive decay law is expressed as:
Nt = No e∧(-λt)

where Nt indicates the quantity of substance at time t, No is the initial amount at t = 0, t is the duration for decay, and λ represents the decay constant.

We need to find Nt:
No = 1.53 mg
λ = ln 2 / 8.04 days = 0.693 / 8.04 days
With t = 13.0 days

When we substitute values,
Nt = 1.53 mg e∧((-0.693/8.04 days) * 13.0 days)
Nt = 0.4989 mg, which rounds to 0.499 mg

Consequently, the mass of the remaining sample after 13.0 days is: 0.499 mg

The correct option is "e"

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