the half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 7 mg.

Question

What was the initial mass (in mg) of the sample?  

What is the mass 6 weeks after the start

Answer 1

Hello Koosi,

One formula that describes radioactive decay is A = A₀ * (1/2)^(t/t_h) where:

A represents the final quantity, A₀ is the initial quantity, t_h is the half-life of the substance, and t is the time that has gone by.

i) What was the initial mass (in mg) of the sample?

You know the final mass here is A = 7 mg, the half life is 4 days, and the time that has gone by is 24 days. The only unknown is the initial mass. Put everything in the equation:

7 = A₀ * (1/2)^(24/4) ---> 7 = A₀ * (1/2)^6 --> A₀ = 7/(1/2)^6. Plug in your calculator: A₀ = 7/(1/2)^6 = 448 mg

ii) What is the mass 6 weeks after the start?

Same equation as before: A = A₀ * (1/2)^(t/t_h)

You know the initial mass (448 mg), the half-life (4 days). You know the time that's gone by: 6 weeks BUT you gotta convert it to days because half-life is in days. so t = 6*7 = 42 days.

Now plug it in to the equation to find A:

A = 448 * (1/2)^(42/4). Plug in your calculator and you'll get the answer.

Cheers.