Question 42.43: A radioactive sample intended for irradiation of a hospital ......

Instructor Solution Manual for Fundamentals of Physics [1361627]
Fundamentals of Physics Extended – Instructor’s Solutions Manual [1360823]

A radioactive sample intended for irradiation of a hospital patient is prepared at a nearby laboratory. The sample has a half-life of 83.61 h. What should its initial activity be if its activity is to be 7.4 × 10 $^8$ Bq when it is used to irradiate the patient 24 h later?

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

Using Eq. 42-16 with Eq. 42-18, we find the initial activity:

$T_{1 / 2}=\frac{\ln 2}{\lambda}=\tau \ln 2$ (42-18)

$R=R_0 e^{-\lambda t} \quad \text { (radioactive decay), }$ (42-16)

$R_0=R e^{t \ln 2 / T_{1 / 2}}=\left(7.4 \times 10^8 \mathrm{~Bq}\right) e^{24 \ln 2 / 83.61}=9.0 \times 10^8 \mathrm{~Bq}$ .

Related Answered Questions

Question: 42.7

What is the nuclear mass density ρm of (a) the fairly low-mass nuclide ^55Mn and (b) the fairly high-mass nuclide ^209Bi? (c) Compare the two answers, with an explanation. What is the nuclear charge density ρq of (d) ^55Mn and (e) ^209Bi? (f) Compare the two answers, with an explanation. ...

Verified Answer:

For

^{55}

Mn the mass density is [la...

Question: 42.48

How much energy is released when a ^238U nucleus decays by emitting (a) an alpha particle and (b) a sequence of neutron, proton, neutron, proton? (c) Convince yourself both by reasoned argument and by direct calculation that the difference between these two numbers is just the total binding energy ...

Verified Answer:

(a) The nuclear reaction is written as

{ }...

Question: 42.46

The radioactive nuclide ^99Tc can be injected into a patient’s bloodstream in order to monitor the blood flow, measure the blood volume, or find a tumor, among other goals. The nuclide is produced in a hospital by a “cow” containing ^99Mo, a radioactive nuclide that decays to ^99Tc with a half-life ...

Verified Answer:

(a) Molybdenum beta decays into technetium: [latex...

Question: 42.42

What is the activity of a 20 ng sample of ^92Kr, which has a half-life of 1.84 s? ...

Verified Answer:

Adapting Eq. 42-21, we have

N_{40}=\left(1...

Question: 42.41

A 1.00 g sample of samarium emits alpha particles at a rate of 120 particles/s. The responsible isotope is ^147Sm, whose natural abundance in bulk samarium is 15.0%. Calculate the half-life. ...

Verified Answer:

The number N of undecayed nuclei present at any ti...

Question: 42.36

Plutonium isotope ^239Pu decays by alpha decay with a half-life of 24 100 y. How many milligrams of helium are produced by an initially pure 12.0 g sample of ^239Pu at the end of 20 000 y? (Consider only the helium produced directly by the plutonium and not by any by-products of the decay process.) ...

Verified Answer:

We have one alpha particle (helium nucleus) produc...

Question: 42.35

A certain radionuclide is being manufactured in a cyclotron at a constant rate R. It is also decaying with disintegration constant λ. Assume that the production process has been going on for a time that is much longer than the half-life of the radionuclide. (a) Show that the number of radioactive ...

Verified Answer:

THINK We modify Eq. 42-11 to take into considerati...

Question: 42.34

Calculate the mass of a sample of (initially pure) ^40K that has an initial decay rate of 1.70 × 10^5 disintegrations/s. The isotope has a half-life of 1.28 × 10^9 y. ...

Verified Answer:

Combining Eqs. 42-20 and 42-21, we obtain

...

Question: 42.33

The air in some caves includes a significant amount of radon gas, which can lead to lung cancer if breathed over a prolonged time. In British caves, the air in the cave with the greatest amount of the gas has an activity per volume of 1.55 × 10^5 Bq/m³. Suppose that you spend two full days ...

Verified Answer:

We note that 3.82 days is 330048 s, and that a bec...

Question: 42.31

Consider an initially pure 3.4 g sample of ^67Ga, an isotope that has a half-life of 78 h. (a) What is its initial decay rate? (b) What is its decay rate 48 h later? ...

Verified Answer:

(a) The decay rate is given by R = λN, where λ is ...