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Chapter 21: Problem 43

Phosphorus- 32 is commonly used in nuclear medicine for the identification of malignant tumors. It decays to sulphur- 32 with a half-life of 14.29 days. If a patient is given 3.5 mg of phosphorus-32, how much phosphorus-32 will remain after 1 month (i.e. 30 days)?

Short Answer

Expert verified
After 1 month (30 days), approximately \(1.4 \, mg\) of phosphorus-32 will remain.

Step by step solution

01

List the given information

We are given the following information: - Initial amount of phosphorus-32 (A₀) = 3.5 mg - Half-life (half_life) = 14.29 days - Time passed (time) = 1 month = 30 days
02

Set up the formula

The radioactive decay formula is given by: Amount remaining (A) = A₀ × (1/2)^(time / half_life) Let's use the given information to plug into the formula.
03

Plug in the given values

Substituting the given values into the radioactive decay formula, we get: A = 3.5 × (1/2)^(30/14.29)
04

Calculate (1/2)^(time / half_life)

(1/2)^(30/14.29) can be calculated as: (1/2)^(2.1) ≈ 0.40
05

Calculate the remaining amount of phosphorus-32

Now that we have the value of (1/2)^(30/14.29), we can find the remaining amount of phosphorus-32 as follows: A ≈ 3.5 × 0.40 = 1.4 mg
06

Final Answer

After 1 month (30 days), approximately 1.4 mg of phosphorus-32 will remain.

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Most popular questions from this chapter

Write balanced equations for each of the following nuclear reactions: $(\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{82}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\( (c) \){ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19} \mathrm{~F}$.

Which are not classified as ionizing radiation: gamma rays, beta particles, radio waves used in radio and television, and infrared radiation from sun?

Which of the following statements about the uranium used in nuclear reactors is or are true? (i) Natural uranium has too little \({ }^{235} \mathrm{U}\) to be used as a fuel. (ii) \({ }^{238} \mathrm{U}\) cannot be used as a fuel because it forms a supercritical mass too easily. (iii) To be used as fuel, uranium must be enriched so that it is more than \(50 \%^{235} \mathrm{U}\) in composition. (iv) The neutron-induced fission of \({ }^{235} \mathrm{U}\) releases more neutrons per nucleus than fission of \({ }^{238} \mathrm{U}\)

Which statement best explains why nuclear transmutations involving neutrons are generally easier to accomplish than those involving protons or alpha particles? (a) Neutrons are not a magic number particle. (b) Neutrons do not have an electrical charge. (c) Neutrons are smaller than protons or alpha particles. (d) Neutrons are attracted to the nucleus even at long distances, whereas protons and alpha particles are repelled.

Chlorine has two stable nuclides, \({ }^{35} \mathrm{Cl}\) and ${ }^{37} \mathrm{Cl}\(. In contrast, \){ }^{36} \mathrm{Cl}$ is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of \({ }^{36} \mathrm{Cl}\) ? (b) Based on the empirical rules about nuclear stability, explain why the nucleus of \({ }^{36} \mathrm{Cl}\) is less stable than either ${ }^{35} \mathrm{Cl}\( or \){ }^{37} \mathrm{Cl}$.
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