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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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BuyFindarrow_forward

Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

The heaviest member of the alkaline earth metals is radium (Ra), a naturally radioactive element discovered by Pierre and Marie Curie in 1898. Radium was initially isolated from the uranium ore pitchblende, in which it is present as approximately 1.0 g per 7.0 metric tons of pitchblende. How many atoms of radium can be isolated from 1.75 × 108 g pitchblende (l metric ton = 1000 kg)? One of the early uses of radium was as an additive to paint so that watch dials coated with this paint would glow in the dark. The longest-lived isotope of radium has a half-life of 1.60 × 103 years. If an antique watch, manufactured in 1925, contains 15.0 mg radium, how many atoms of radium will remain in 2025?

Interpretation Introduction

Interpretation: It is given that, radon is present as 1.0g per 7.0metricton of a pitch ball. The number of radon atoms that can be isolated from given mass of pitch-blende is to be calculated. The number of radon atoms remain in 2025 is to be calculated if 15mg radon is manufactured in 1925 .

Concept introduction: Amount of radon left is calculated using the formula,

AE=A00.5t/t1/2

To determine: The number of radon atoms that can be isolated from 1.75×108g pitch-blende; the number of radon atoms remain in 2025 , if 15mg radon is manufactured in 1925 .

Explanation

Mass of radon (Ra) is 25g_ .

Given

Mass of pitch-blende is 1.75×108g .

The conversion of gram (g) into kilogram (kg) is done as,

1g=103kg

Hence,

The conversion of 1.75×108g into kilogram is,

1.75×108g=(1.75×108×103)kg=1.75×105kg

Since, radon is present as 1.0g per 7.0metricton of a pitch ball, mass of radon is calculated as,

MassofRa=Massofpitch-blende×1.0gRa7.0metricton×(1metricton1000kg)

Substitute the value of mass of pitch-blende in the above equation.

MassofRa=Massofpitch-blende×1.0gRa7.0metricton×(1metricton1000kg)=1.75×105kg×1.0gRa7.0metricton×(1metricton1000kg)=25g_

Number of radon (Ra) atoms that can be isolated from 1.75×108g pitch-blende is 6.66×1022atoms_ .

Mass of radon is 25g .

Atomic mass of radon is 226g .

Formula

The number of radon atoms is calculated as,

AtomsofRa=MassofRa×1molRaAtomicmassofRa×6.022×1023atoms1molRa

Substitute the values of mass and atomic mass of radon in the above equation.

AtomsofRa=MassofRa×1molRaAtomicmassofRa×6.022×1023atoms1molRa=25g×1molRa226.0g×6.022×1023atoms1molRa=6.66×1022atoms_

Number of radon (Ra) atoms in 15mg is 3

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