CHEMISTRY:ATOMS-FOCUSED..-ACCESS
CHEMISTRY:ATOMS-FOCUSED..-ACCESS
2nd Edition
ISBN: 9780393615319
Author: Gilbert
Publisher: NORTON
Question
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Chapter 21, Problem 21.47QA
Interpretation Introduction

To find:

a) The balanced nuclear equation for decay of C 11.

b) The binding energy of C 11..

Expert Solution & Answer
Check Mark

Answer to Problem 21.47QA

Solution:

a) Balanced nuclear equation for decay of C 11 is

CB+Β10511611

b) The binding energy of C 11 is 1.176 ×10-11J.

Explanation of Solution

1) Concept:

First, we will balance the nuclear equation for decay of C 11 by using the emission of beta particles. To determine the binding energy of C 11, we need to calculate the mass decay of C 11. From the mass decay and Albert Einstein equation, we will calculate the binding energy.

2) Formula:

Albert Einstein equation for the binding energy.

BE=(m)c2

3) Given:

i) The exact mass of C 11 is 1.82850×10-26 kg.

ii) 1 J = 1 kg ms2

iii)   Mass of proton = 1.67262×10-27kg

iv)  Mass of neutrons = 1.67493×10-27kg

v) Mass of electrons = 9.10939×10-31kg

vi) Speed of light c = 2.998 ×108m/s

4) Calculation:

a) C 11 isotope of carbon undergoes positron emission.

The balanced equation for decay of C 11,

CB+Β10511611

b) The binding energy is calculated using Albert Einstein equation and exact mass of C 11 is 1.82850×10-26 kg

To calculate the mass of the nucleons, we have to subtract the mass of 6 electrons from exact mass

C 11: (1.82850×10-26 kg)  6(9.10939×10-31kg)

C 11: = 1.827953×10-26 kg

Now, we calculate the mass of neutrons and protons present in the one atom of C 11

mass of C 11 : (6 protons ×1.67262×10-27kgprotons) + (5 neutrons ×1.67493×10-27kgneutrons)

mass of C 11 : (1.003572×10-26 kg) + (8.37465×10-27 kg) 

mass of C 11=1.841037 ×10-26 kg

Now, calculate the mass defect (m) from the exact mass of the nucleus of C 11 and its subatomic particles.

m = mass of nucleus  mass of nucleons 

m=1.841037 ×10-26 kg- 1.827953×10-26 kg 

m=1.308356 ×10-28kg

Now, calculate the binding energy (BE) by using Albert Einstein equation

BE =(m)c2

BE =1.308356 ×10-28kg × 2.998 ×108ms2

BE =1.17595 ×10-11kg m2s2 × 1 Jkg m2s2 =1.176 ×10-11J

BE =1.176 ×10-11J

Conclusion:

We determined the balanced nuclear equation and calculated the binding energy from the exact mass and mass defect.

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Chapter 21 Solutions

CHEMISTRY:ATOMS-FOCUSED..-ACCESS

Ch. 21 - Prob. 21.11VPCh. 21 - Prob. 21.12VPCh. 21 - Prob. 21.13QACh. 21 - Prob. 21.14QACh. 21 - Prob. 21.15QACh. 21 - Prob. 21.16QACh. 21 - Prob. 21.17QACh. 21 - Prob. 21.18QACh. 21 - Prob. 21.19QACh. 21 - Prob. 21.20QACh. 21 - Prob. 21.21QACh. 21 - Prob. 21.22QACh. 21 - Prob. 21.23QACh. 21 - Prob. 21.24QACh. 21 - Prob. 21.25QACh. 21 - Prob. 21.26QACh. 21 - Prob. 21.27QACh. 21 - Prob. 21.28QACh. 21 - Prob. 21.29QACh. 21 - Prob. 21.30QACh. 21 - Prob. 21.31QACh. 21 - Prob. 21.32QACh. 21 - Prob. 21.33QACh. 21 - Prob. 21.34QACh. 21 - Prob. 21.35QACh. 21 - Prob. 21.36QACh. 21 - Prob. 21.37QACh. 21 - Prob. 21.38QACh. 21 - Prob. 21.39QACh. 21 - Prob. 21.40QACh. 21 - Prob. 21.41QACh. 21 - Prob. 21.42QACh. 21 - Prob. 21.43QACh. 21 - Prob. 21.44QACh. 21 - Prob. 21.45QACh. 21 - Prob. 21.46QACh. 21 - Prob. 21.47QACh. 21 - Prob. 21.48QACh. 21 - Prob. 21.49QACh. 21 - Prob. 21.50QACh. 21 - Prob. 21.51QACh. 21 - Prob. 21.52QACh. 21 - Prob. 21.53QACh. 21 - Prob. 21.54QACh. 21 - Prob. 21.55QACh. 21 - Prob. 21.56QACh. 21 - Prob. 21.57QACh. 21 - Prob. 21.58QACh. 21 - Prob. 21.59QACh. 21 - Prob. 21.60QACh. 21 - Prob. 21.61QACh. 21 - Prob. 21.62QACh. 21 - Prob. 21.63QACh. 21 - Prob. 21.64QACh. 21 - Prob. 21.65QACh. 21 - Prob. 21.66QACh. 21 - Prob. 21.67QACh. 21 - Prob. 21.68QACh. 21 - Prob. 21.69QACh. 21 - Prob. 21.70QACh. 21 - Prob. 21.71QACh. 21 - Prob. 21.72QACh. 21 - Prob. 21.73QACh. 21 - Prob. 21.74QACh. 21 - Prob. 21.75QACh. 21 - Prob. 21.76QACh. 21 - Prob. 21.77QACh. 21 - Prob. 21.78QACh. 21 - Prob. 21.79QACh. 21 - Prob. 21.80QACh. 21 - Prob. 21.81QACh. 21 - Prob. 21.82QACh. 21 - Prob. 21.83QACh. 21 - Prob. 21.84QACh. 21 - Prob. 21.85QACh. 21 - Prob. 21.86QACh. 21 - Prob. 21.87QACh. 21 - Prob. 21.88QACh. 21 - Prob. 21.89QACh. 21 - Prob. 21.90QACh. 21 - Prob. 21.91QACh. 21 - Prob. 21.92QACh. 21 - Prob. 21.93QACh. 21 - Prob. 21.94QACh. 21 - Prob. 21.95QACh. 21 - Prob. 21.96QACh. 21 - Prob. 21.97QACh. 21 - Prob. 21.98QACh. 21 - Prob. 21.99QACh. 21 - Prob. 21.100QACh. 21 - Prob. 21.101QACh. 21 - Prob. 21.102QACh. 21 - Prob. 21.103QACh. 21 - Prob. 21.104QACh. 21 - Prob. 21.105QACh. 21 - Prob. 21.106QACh. 21 - Prob. 21.107QACh. 21 - Prob. 21.108QACh. 21 - Prob. 21.109QACh. 21 - Prob. 21.110QACh. 21 - Prob. 21.111QACh. 21 - Prob. 21.112QACh. 21 - Prob. 21.113QACh. 21 - Prob. 21.114QACh. 21 - Prob. 21.115QACh. 21 - Prob. 21.116QACh. 21 - Prob. 21.117QACh. 21 - Prob. 21.118QACh. 21 - Prob. 21.119QACh. 21 - Prob. 21.120QACh. 21 - Prob. 21.121QACh. 21 - Prob. 21.122QACh. 21 - Prob. 21.123QACh. 21 - Prob. 21.124QACh. 21 - Prob. 21.125QACh. 21 - Prob. 21.126QACh. 21 - Prob. 21.127QACh. 21 - Prob. 21.128QACh. 21 - Prob. 21.129QACh. 21 - Prob. 21.130QA
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