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 48E

(a)

To determine

Reason why exposure inversely varies with square of distance from source.

(a)

Expert Solution
Check Mark

Answer to Problem 48E

The exposure varies inversely with distance from source because the flux of radiation is inversely proportional to the distance.

Explanation of Solution

Exposure to radiation is defined by extent of dose that is received by matter. The radiation energy is continuously distributed in all direction at a certain distance from radiating source.

The flux of radiation is defined as amount of radiation per unit area per unit time. If a spherical region of radius same as distance from source is imagined, then the flux of radiation inversely varies with distance because area of sphere is directly proportional to square of its radius.

Thus, the exposure which is a measure of flux also varies inversely with square of distance.

Conclusion:

Thus, exposure varies inversely with distance from source because the flux of radiation is inversely proportional to the distance.

(b)

To determine

Time required to produce dose of 100rems at distance 0.01m.

(b)

Expert Solution
Check Mark

Answer to Problem 48E

The time required to produce dose of 100rems at distance 0.01m is 758.25s.

Explanation of Solution

A dose of 8.2rads is produced by 1mg of radium per hour at distance 0.01m. For gamma rays of radium the quality factor is 0.965.

Write the expression of biologically equivalent dose D of 1mg radium source

  D=AQ        (I)

Here, A is absorbed dose in rads and Q is quality factor.

Write the expression of required time for second radium source

  T1=(D1D)(MM1)(R12R2)T        (II)

Here, D1 is dose produced by second source of mass M1 at distance R1 and M is mass of first radium source that produces dose D at distance R over time T.

Conclusion:

Substitute 8.2rads for A and 0.965 for Q in expression (I)

  D=(8.2rads)(0.965)=7.913rems

Substitute 7.913rems for D, 100rems for D1, 0.01m for R1 and R, 1hour for T, 1mg for M and 60mg for M1 in expression (II)

  T1=(100rems7.913rems)(1mg60mg)((0.01m)2(0.01m)2)(1hour(3600s1hour))=758.25s

Thus, the time required to produce dose of 100rems at distance 0.01m is 758.25s.

(c)

To determine

Time required to produce dose of 100rems at distance 0.05m.

(c)

Expert Solution
Check Mark

Answer to Problem 48E

The time required to produce dose of 100rems at distance 0.05m is 18956.15s.

Explanation of Solution

Write the expression of required time for third radium source

  T2=(D2D)(MM2)(R22R2)T        (III)

Here, D2 is dose produced by third source of mass M2 at distance R2.

Conclusion:

Substitute 7.913rems for D, 100rems for D2, 0.01m for R, 0.05m for R2, 1hour for T, 1mg for M and 60mg for M2 in expression (III)

  T2=(100rems7.913rems)(1mg60mg)((0.05m)2(0.01m)2)(1hour(3600s1hour))=18956.15s

Thus, the time required to produce dose of 100rems at distance 0.05m is 18956.15s.

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