Chapter 19.2, Problem 4RQ

(a)

Interpretation Introduction

Interpretation: The radiotracer having shortest half-life using graph has to be identified.

Concept introduction: In a nuclear reaction, unstable nuclide disintegrates into stable nuclide with emission of various radiations spontaneously. It is called radioactivity of nucleus. Emission of rays like alpha, beta and gamma rays occur in the process which changes the identity of nucleus.

During a nuclear change, an element undergoes change in its atomic mass or atomic number or both by emission of charged particles such as beta particle, alpha particle. Beta particle is one that has unit negative charge and alpha particle is one that has 2 unit positive charges and is equivalent to helium atom ${}_2^4\text{He}$ . Emission of proton, beta particle, alpha particle causes a change in atomic number of element.

Answer to Problem 4RQ

Mo-99 has the shortest half life.

Explanation of Solution

Time needed for original or initial sample of radioactive element to decay to its half quantity or concentration is known as half-life time.

The formula to calculate half life ( $T$) is as follows:

  $T=\frac{t}{n}$

Where,

  $n$ is number of half lives.

  $t$ is the elapsed time.

  $T$ is the half life of radioactive nucleus.

For the graph shown for half life in days versus the radioactive element, it is clear that the half lives of elements are as follows:

I-131 has half life of 8 days. Similarly for Mo-99, P-32 and Xe-133 half lives are 3 days, 14 days and 5 days approximately; respectively.

So the shortest half life is for Mo-99.

(b)

Interpretation Introduction

Interpretation: The radiotracer having half-life equal to sum of half lives of Xe-133 and Mo-99 using graph has to be identified.

Concept introduction: In a nuclear reaction, unstable nuclide disintegrates into stable nuclide with emission of various radiations spontaneously. It is called radioactivity of nucleus. Emission of rays like alpha, beta and gamma rays occur in the process which changes the identity of nucleus.

During a nuclear change, an element undergoes change in its atomic mass or atomic number or both by emission of charged particles such as beta particle, alpha particle. Beta particle is one that has unit negative charge and alpha particle is one that has 2 unit positive charges and is equivalent to helium atom ${}_2^4\text{He}$ . Emission of proton, beta particle, alpha particle causes a change in atomic number of element.

Answer to Problem 4RQ

The radiotracer having half-life equal to sum of half lives of Xe-133 and Mo-99 is I-131.

Explanation of Solution

Time needed for original or initial sample of radioactive element to decay to its half quantity or concentration is known as half-life time.

The formula to calculate half life ( $T$) is as follows:

  $T=\frac{t}{n}$

Where,

  $n$ is number of half lives.

  $t$ is the elapsed time.

  $T$ is the half life of radioactive nucleus.

For the graph shown for half life in days versus the radioactive element, it is clear that the half lives of elements are as follows:

I-131 has half life of 8 days. Similarly for Mo-99, P-32 and Xe-133 half lives are 3 days, 14 days and 5 days approximately; respectively.

On addition of half lives of Mo-99 and Xe-133 result comes out to be 8 days which is equal to half life of I-131.

(c)

Interpretation Introduction

Interpretation: The radiotracer will be left in least quantity after 15 days, using graph has to be identified.

Concept introduction: In a nuclear reaction, unstable nuclide disintegrates into stable nuclide with emission of various radiations spontaneously. It is called radioactivity of nucleus. Emission of rays like alpha, beta and gamma rays occur in the process which changes the identity of nucleus.

During a nuclear change, an element undergoes change in its atomic mass or atomic number or both by emission of charged particles such as beta particle, alpha particle. Beta particle is one that has unit negative charge and alpha particle is one that has 2 unit positive charges and is equivalent to helium atom ${}_2^4\text{He}$ . Emission of proton, beta particle, alpha particle causes a change in atomic number of element.

Answer to Problem 4RQ

As per the graph, Mo-99 will be left with least quantity after 15 days.

Explanation of Solution

Time needed for original or initial sample of radioactive element to decay to its half quantity or concentration is known as half-life time.

For the graph shown for half life in days versus the radioactive element, it is clear that the half lives of elements are as follows:

I-131 has half life of 8 days. Similarly for Mo-99, P-32 and Xe-133 half lives are 3 days, 14 days and 5 days approximately; respectively.

As per the graph, Mo-99 will be left with least quantity after 15 days. This is so because its half life is 3 days, it will take 3 days to get reduced to half of its original sample. So nearly 6 days will be required to get consumed nearly full.

(d)

Interpretation Introduction

Interpretation: The radiotracer will be left in greatest quantity after 15 days, using graph has to be identified.

Concept introduction: In a nuclear reaction, unstable nuclide disintegrates into stable nuclide with emission of various radiations spontaneously. It is called radioactivity of nucleus. Emission of rays like alpha, beta and gamma rays occur in the process which changes the identity of nucleus.

During a nuclear change, an element undergoes change in its atomic mass or atomic number or both by emission of charged particles such as beta particle, alpha particle. Beta particle is one that has unit negative charge and alpha particle is one that has 2 unit positive charges and is equivalent to helium atom ${}_2^4\text{He}$ . Emission of proton, beta particle, alpha particle causes a change in atomic number of element.

Answer to Problem 4RQ

As per the graph, P-32 will be left with greatest quantity after 15 days.

Explanation of Solution

Time needed for original or initial sample of radioactive element to decay to its half quantity or concentration is known as half-life time.

For the graph shown for half life in days versus the radioactive element, it is clear that the half lives of elements are as follows:

I-131 has half life of 8 days. Similarly for Mo-99, P-32 and Xe-133 half lives are 3 days, 14 days and 5 days approximately; respectively.

As per the graph, P-32 will be left in greatest quantity after 15 days. This is so because its half life is 14 days approximately; it will take 14 days to get reduced to half of its original sample. So nearly 28 days more will be required to get consumed nearly full. Whereas I-131, Xe-133 and Mo-99 will require 16 days, 10 days and 6 days to consumed nearly completely respectively.