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

What are the factors that affect demand for a commodity

Florence Reply

differentiate between demand and supply giving examples

Lambiv Reply

differentiated between demand and supply using examples

Lambiv

what is labour ?

Lambiv

how will I do?

Venny Reply

how is the graph works?I don't fully understand

Rezat Reply

information

Eliyee

devaluation

Eliyee

WARKISA

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Lambiv

multiple choice question

Aster Reply

appreciation

Eliyee

explain perfect market

Lindiwe Reply

In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,

Ezea

What is ceteris paribus?

Shukri Reply

other things being equal

AI-Robot

When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab

Kelo

Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)

Kelo

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Shukri

Can I ask you other question?

Shukri

what is monopoly mean?

Habtamu Reply

What is different between quantity demand and demand?

Shukri Reply

Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded

Ezea

Shukri

how do you save a country economic situation when it's falling apart

Lilia Reply

what is the difference between economic growth and development

Fiker Reply

Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.

Shukri

production function means

Jabir

What do you think is more important to focus on when considering inequality ?

Abdisa Reply

any question about economics?

Awais Reply

sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏

Asui

it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs

Awais

thank you so much 👍 sir

Asui

In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p

Cornelius

Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .

Feyisa Reply

Answer

Feyisa

Jabir

the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema

Gsbwnw Reply

suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product

Abdureman

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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?