Explanation Given data: The patient’s weight is 75 kg, The activity of beta-emitter swallowed is 30 μCi , Half-life of the beta emitter is 5 days, Average energy of the beta particle is 0.35 MeV, and Energy absorbed is 90%. Formula used: Write the expression for number of nuclei decayed after time t. N = N 0 ( 1 2 ) t t 1 2 (1) Here, N is the number of atoms remaining after time t , N 0 is the number of atoms at the start at t = 0 , t is the time, and t 1 2 is the half-life. Write the expression for radioactivity. R = 0.693 N t 1 2 (2) Here, R is the activity, t 1 2 is the half-life, and N is the number of atoms remaining after time t. Explanation: Consider the conversion factor, 1 Ci = 3.7 × 10 10 Bq Convert the value using conversion factor. 30 × 10 − 6 Ci = ( 3.7 × 10 10 Bq ) ( 30 × 10 − 6 C ) 1 Ci = 1.11 × 10 6 Bq Convert 5days into seconds. 5 d = 5 ( 1 d ) = 5 × 86 , 400 s { ∵ 1 d = 86 , 400 s } = 432,000 s The decay rate of radioactive atom is considered as follows. r = 1 τ = ln 2 t 1 2 (3) Substitute 432,000 s for t 1 2 in equation (3), r = ln 2 432 , 000 s = 0.693 432 , 000 s = 1.605 × 10 − 6 s − 1 Rearrange equation (2) to solve for N . N = R t 1 2 0.693 (4) Substitute equation (3) in equation (4), N = R r (5) Substitute 1.11 × 10 6 Bq for R and 1.605 × 10 − 6 s − 1 for r in equation (5), N = 1.11 × 10 6 Bq 1.605 × 10 − 6 s − 1 = 6.92 × 10 11 Subtract equation (1) with N 0 to find the number of decay in one week, N 0 − N = N 0 ( 1 − ( 1 2 ) t t 1 2 ) (6) Substitute 6

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Radioactive decay

The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. T…

Artificial Radioactivity

The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.

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Chapter 30, Problem 55P

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The dose equivalent patient receives in first week.

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Chapter 30, Problem 54P

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Chapter 30 Solutions

College Physics: A Strategic Approach (4th Edition)

Ch. 30 - Prob. 1CQ Ch. 30 - Prob. 2CQ Ch. 30 - Prob. 3CQ Ch. 30 - Prob. 4CQ Ch. 30 - Prob. 5CQ Ch. 30 - Prob. 6CQ Ch. 30 - Figure Q30.7 shows how the number of nuclei of one...Ch. 30 - Prob. 8CQ Ch. 30 - Prob. 9CQ Ch. 30 - Prob. 10CQ

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The dose equivalent patient receives in first week.

Solution Summary: The author explains how the dose equivalent patient receives in first week is 0.29 mSv.

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