Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

49 After decaying for 48 hours, l/16 of the original mass of a radioisotope sample remains unchanged. What is the half-life of this radioisotope?
(1) 3.0 h (3) 12 h(2) 9.6 h (4) 24 h


Sagot :

1/16 left would imply 4 half lives have passed (1/2 left = 1, 1/4 left = 2, 1/8 left = 3, 1/16 left = 4). So 4 half lives passed in 48 hours, meaning dividing 48 by 4 will give you the length of 1 half life. Which in this case is 12 hours.

Answer:

The half life of the radioisotope is 12 hours.

Explanation:

Initial mass of the radioisotope = x

Final mass of  the radioisotope = [tex]\frac{1}{16}\times x[/tex] = 0.0625x

Half life of the radioisotope =[tex]t_{\frac{1}{2}}[/tex]

Age of the radioisotope = t = 48 hours

Formula used :

[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]

where,

[tex]N_o[/tex] = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope

[tex]\lambda[/tex] = rate constant

[tex]N=N_o\times e^{-(\frac{0.693}{t_{1/2}})\times t}[/tex]

Now put all the given values in this formula, we get

[tex]0.0625x=x\times e^{-(\frac{0.693}{t_{1/2}})\times 48 h}[/tex]

[tex]\ln(0.0625) \times \frac{1}{(-0.693\times 48 h)}=\frac{1}{t_{1/2}}[/tex]

[tex]t_{1/2} = 11.99 hours = 12 hours[/tex]

The half life of the radioisotope is 12 hours.

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.