The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced to a mass of 7 mg. Round your answers to 5 decimal places as needed.

Question

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

What is the mass 5 weeks after the start? _______________

(Step by step is much appreciated)

Answer 1

.5= e^4r

ln.5 = 4r

r=ln.5/4

7= Po(e^20r)

Po = original amount = 7/e^5ln.5

or

7 in 20 days

14 in 16

28 in 12

56 in 8

112 in 4

224 mg originally

in 5 weeks that's 35 days

3.5 in 24 days

1.75 in 28 days

.875 in 32 days

.4375 mg in 36 days

in 35 days, a little more

Answer 2

Hi Vincent P

Question for you since there are several ways that can be applied I was wondering is there a formula in your text as part of your class for you to use maybe one of these formulas for Half Life?

N(t) = N₀(1/2)^t/(t/2)

Where

N(t) = Mass after time t (quantity of the remaining substance)

N₀ = Initial mass

t_1/2 = half life of the substance

t = t elapsed

or

A = A₀(1/2)^t/h

Where

A = Mass after time t (quantity remaining) or even final amount

A₀ = Initial mass

t = time elapsed

h = half life

I asked because your numbers plug into either of these quite directly so that you can solve for the missing part.

A = 7

t = 20 days

h = 4 days

So A₀

7/(1/2)^20/4 = 7/(1/2)⁵ = 7/(1/32) = 7 * 32= 224 mg

Checking

224(1/2)^20/4 = 224(1/2)⁵ = 224*1/32 = 224/32 = 7

I hope this helps let me know. If you are using a formula like the one above, can you continue and do the next part.