The half-life of 237U is 6.75 days. Starting with a 50 mg sample, how much would be left after 54 days?

Answer 1

Solving for half life means that you need to set up an exponential decay equation. The general equation is as follows:

A = A₀(1/2)^t/h

where:

1. A = final amount
2. A₀ = initial amount
3. t = time
4. h = half-life time

You can solve the question by plugging in the values from your question into the equation where...

1. A = ???
2. A₀ = 50 mg
3. t = 54 days
4. h = 6.75 days

A = A₀(1/2)^t/h

A = 50(1/2)^54/6.75

A = 50(1/2)⁸

A = 50(1/256)

A = 0.1953...

The final answer would be that 0.195 mg of 237U will be left after 54 days. Hope this helps!

Answer 2

FR = 0.5ⁿ

FR = fraction remaining = ?

n = number of half lives that have elapsed = 54 days x 1 half life/6.75 days = 8 half lives have elapsed

FR = 0.5⁸

FR = 0.003906 which is the fraction remaining

Converting this to mg, we have 50 mg x 0.003906 = 0.195 mg = 0.2 mg (1 sig. fig. based on 50 mg value)