Question

(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=

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 = t_1/2 = ln2/K = 7.21 s