General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 31, Problem 55E

(a)

To determine

Number of excess thyroid cancers induced by explosions.

(a)

Expert Solution
Check Mark

Answer to Problem 55E

The number of excess thyroid cancers induced by explosions was 4.30.

Explanation of Solution

Nuclear explosions in atmosphere caused average thyroid dose of 3.1×104rad to 2.2×108persons.

Write the expression of collective dose D received

  D=pd        (I)

Here, p is total population and d is average thyroid dose.

Since 63 cancers are induced per 106person rads of thyroid dose therefore the number of excess cancers is:

  n=D(63)(106person rads)        (II)

Conclusion:

Substitute 3.1×104rad for d and 2.2×108persons for p in expression (I)

  D=(2.2×108persons)(3.1×104rad)=6.82×104person rads

Substitute 6.82×104person rads for D in expression (II)

  n=(6.82×104person rads)(63)(106person rads)=4.30

Thus, the number of excess thyroid cancers induced by explosions was 4.30.

(b)

To determine

Fractional increase in present rate of thyroid cancers.

(b)

Expert Solution
Check Mark

Answer to Problem 55E

The fractional increase in present rate of thyroid cancers is 1.14×105.

Explanation of Solution

Write the expression of number of thyroid cancers in 45 years due to present rate

  N=r(45year)        (III)

Here, r is present rate of thyroid cancer per year.

Write the expression of fractional increase in present rate

  f=nN        (IV)

Here, f is the fractional increase in percent and N is the number of thyroid cancer cases.

Conclusion:

Substitute 8400year1 for r in expression (III).

  N=(8400year)(45year)=378000

Substitute 378000 for N and 4.30 for n in expression (IV).

  f=(4.30)(378000)=1.14×105

Thus, the fractional increase in present rate of thyroid cancers is 1.14×105.

(c)

To determine

Chance that an infant develops thyroid cancer.

(c)

Expert Solution
Check Mark

Answer to Problem 55E

The chance that an infant develops thyroid cancer is 1.26×106.

Explanation of Solution

Thyroid doses received by infants are of 0.02rad.

Since 63 cancers are induced per 106person rads of thyroid dose therefore the chances P of an infant developing cancer is:

  P=i(63)(106person rads )        (V)

Here, i is collective dose received by infants.

Conclusion:

Since risk for infants is same as for whole populations therefore the value of i for an individual infant is:

  i=(0.02rad)(1person)=0.02person rad

Substitute 0.02person rad for i in expression (V)

  P=(0.02person rad)(63)(106person rads )=1.26×106

Thus, an infant has chance 1.26×106 of developing thyroid cancer.

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