Question

(a) Chromium-51 is a radioisotope that is used to assess the lifetime of red blood cells...

(a) Chromium-51 is a radioisotope that is used to assess the lifetime of red blood cells The half-life of chromium-51 is 27.7 days. If you begin with 32.8 mg of this isotope, what mass remains after 70.6 days have passed? Since the decomposition is a radioactive decay reaction, it is first order.

mg=

(b)What is the half-life of aluminum-25 if 19.2 seconds are required for the mass of a sample of aluminum-25 to fall to 15.8 percent of its original value? Since the decomposition is a radioactive decay reaction, it is first order.

seconds=

Homework Answers

Answer #1

If the reaction follows 1st order

ln[A]0/[A] = Kt

[A]0 = initial mass

[A] = final mass

K = rate constant

t = time

half life is when the initial mass reduced to half

[A]1/2 = [A]0/2

ln[A]0/[A]0/2 = 27.7 days x K

K = 0.02502336 days-1

for [A]0 = 32.8 mg

ln32.8 mg/[A] = 0.02502336 days-1 x 70.6 days

3.49 - ln[A] = 1.766

ln[A] = 1.72335

[A] = 5.6 mg

(b)similarly as a

[A] = 15.8/100 x [A]0

   = 0.158[A]0

putting in equation ln[A]0/0.158[A]0 = K x 19.2 s

K = 1.84516 / 19.2 s = 0.0961 s-1

half life = t1/2 = ln2/K = 7.21 s

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