Answer:
Activity of Sr isotope is [tex]2.6217\times 10^{11} atom/s[/tex].
Explanation:
Mass of the Sr isotope = 50 mg =0.050 g
Moles of Sr isotope = [tex]\frac{0.050 g}{87.62 g/mol}=5.7064\times 10^{-4} mol[/tex]
Number atoms of of Sr isotope:
[tex]5.7064\times 10^{-4} mol\times 6.022\times 10^{23} atoms=3.4364\times 10^{20} atoms[/tex]
Half life of the Sr = [tex]t_{1/2}=28.8 years= 9.08352\times 10^{8} s[/tex]
[tex]1 year =3.154\times 10^{7} seconds[/tex]
Activity of the Sr isotope = k
[tex]k=\frac{0.693}{t_{1/2}}=\frac{0.693}{9.08352\times 10^{8} s}=7.629\times 10^{-10} s^{-1}[/tex]
Activity in atom/second:
= Number of atoms × k
[tex]=3.4364\times 10^{20} atoms\times 7.629\times 10^{-10} s^{-1}[/tex]
[tex]=2.6217\times 10^{11} atom/s[/tex]
