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Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

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BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

Phosphorus occurs in nature as a single isotope, phosphorus-31. Neutron irradiation of phosphorus-31 produces phosphorus-32, a β emitter with a half-life of 14.28 days. Assume you have a sample containing phosphorus-32 that has a rate of decay of 3.2 × 106 dpm. Draw a graph showing disintegrations per minute as a function of time during a period of 1 year.

Interpretation Introduction

Interpretation: To draw the graph of disintegration per minute as a function of time during a period of one year.

Concept Introduction: Phosphorus-31 occurs in nature as a single isotope of phosphorus. Phosphorus produces phosphorus-32 by the emission of beta particle.

Half-Life: It is defined as the time required to reduce the concentration of reactant present in the reaction to one half of its initial value.

Explanation

Half-life of the phosphorus-32(t1/2) =14.28days

The rate of decay A0= 3.2×106dpm

The time period (T) = 1year.

According to integrated first order rate equation,

ln[A] = -Kt + ln[A0]

K = 0.693t1/2

K=0.69314.28=4.854×10-2days-1

=[4

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