10.7 Medical applications and biological effects of nuclear radiation (Page 5/18)

University physics volume 3 Page 5 / 18

Typical doses received during diagnostic x-ray exams
Procedure	Effective Dose (mSv)
Chest	0.02
Dental	0.01
Skull	0.07
Leg	0.02
Mammogram	0.40
Barium enema	7.0
Upper GI	3.0
CT head	2.0
CT abdomen	10.0

What mass of $^{137} Cs$ Escaped chernobyl?

The Chernobyl accident in Ukraine (formerly in the Soviet Union) exposed the surrounding population to a large amount of radiation through the decay of

^{137} Cs

. The initial radioactivity level was approximately

A = 6.0 MCi .

Calculate the total mass of

^{137} Cs

involved in this accident.

Strategy

The total number of nuclei, N , can be determined from the known half-life and activity of

^{137} Cs

(30.2 y). The mass can be calculated from N using the concept of a mole.

Solution

Solving the equation

A = \frac{0.693 N}{t_{1 / 2}}

for N gives

N = \frac{A t_{1 / 2}}{0.693} .

Entering the given values yields

N = \frac{(6.0 MCi) (30.2 y)}{0.693} .

To convert from curies to becquerels and years to seconds, we write

N = \frac{(6.0 \times 10^{6} Ci) (3.7 \times 10^{10} Bq/Ci) (30.2 y) (3.16 \times 10^{7} s/y)}{0.693} = 3.1 \times 10^{26} .

One mole of a nuclide $^{A} X$ has a mass of A grams, so that one mole of $^{137} Cs$ has a mass of 137 g. A mole has $6.02 \times 10^{23}$ nuclei. Thus the mass of $^{137} Cs$ released was

m = (\frac{137 g}{6.02 \times 10^{23}}) (3.1 \times 10^{26}) = 70 \times 10^{3} g = 70 kg .

Significance

The mass of

^{137} Cs

involved in the Chernobyl accident is a small material compared to the typical amount of fuel used in a nuclear reactor. However, approximately 250 people were admitted to local hospitals immediately after the accident, and diagnosed as suffering acute radiation syndrome. They received external radiation dosages between 1 and 16 Sv. Referring to biological effects in [link] , these dosages are extremely hazardous. The eventual death toll is estimated to be around 4000 people, primarily due to radiation-induced cancer.

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Check Your Understanding Radiation propagates in all directions from its source, much as electromagnetic radiation from a light bulb. Is activity concept more analogous to power, intensity, or brightness?

power

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Summary

Nuclear technology is used in medicine to locate and study diseased tissue using special drugs called radiopharmaceuticals. Radioactive tags are used to identify cancer cells in the bones, brain tumors, and Alzheimer’s disease, and to monitor the function of body organs, such as blood flow, heart muscle activity, and iodine uptake in the thyroid gland.
The biological effects of ionizing radiation are due to two effects it has on cells: interference with cell reproduction and destruction of cell function.
Common sources of radiation include that emitted by Earth due to the isotopes of uranium, thorium, and potassium; natural radiation from cosmic rays, soils, and building materials, and artificial sources from medical and dental diagnostic tests.
Biological effects of nuclear radiation are expressed by many different physical quantities and in many different units, including the rad or radiation dose unit.

Key equations

Atomic mass number	$A = Z + N$
Standard format for expressing an isotope	$_{Z}^{A} X$
Nuclear radius, where r ₀ is the radius of a single proton	$r = r_{0} A^{1 / 3}$
Mass defect	$Δ m = Z m_{p} + (A - Z) m_{n} - m_{nuc}$
Binding energy	$E = (Δ m) c^{2}$
Binding energy per nucleon	$B E N = \frac{E_{b}}{A}$
Radioactive decay rate	$- \frac{d N}{d t} = λ N$
Radioactive decay law	$N = N_{0} e^{− λ t}$
Decay constant	$λ = \frac{0.693}{T_{1 / 2}}$
Lifetime of a substance	$\bar{T} = \frac{1}{λ}$
Activity of a radioactive substance	$A = A_{0} e^{− λ t}$
Activity of a radioactive substance (linear form)	$ln A = − λ t + ln A_{0}$
Alpha decay	$_{Z}^{A} X \to_{Z - 2}^{A - 4} X +_{2}^{4} H e$
Beta decay	$_{Z}^{A} X \to_{Z + 1}^{A} X +_{−1}^{0} e + \bar{v}$
Positron emission	$_{Z}^{A} X \to_{Z - 1}^{A} X +_{+ 1}^{0} e + v$
Gamma decay	$_{Z}^{A} X * \to_{Z}^{A} X + γ$

Questions & Answers

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While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma

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Not really sure

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to drain extracellular fluid all over the body.

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The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of

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to transport fluids fats proteins and lymphocytes to the blood stream as lymph

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Anatomy is the identification and description of the structures of living things

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Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.

AI-Robot

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Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems

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Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)

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Source: OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4

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10.7 Medical applications and biological effects of nuclear radiation (Page 5/18)

What mass of 137 Cs Escaped chernobyl?

Strategy

Solution

Significance

Summary

Key equations

Questions & Answers

Read also:

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What mass of $^{137} Cs$ Escaped chernobyl?