$A$ nucleus with mass number $A = 240$ and binding energy per nucleon $= 7.6 \,MeV$ breaks into two fragments each of $A = 120$ with binding energy per nucleon $= 8.5 \,MeV$. Calculate the released energy.
(216 MEV) The binding energy of the parent nucleus with $A = 240$ is given by:
$E_{b1} = 240 \times 7.6 \,MeV = 1824 \,MeV$
The binding energy of the two daughter fragments,each with $A = 120$,is given by:
$E_{b2} = 2 \times (120 \times 8.5 \,MeV) = 2 \times 1020 \,MeV = 2040 \,MeV$
The energy released in the process is the difference between the total binding energy of the products and the binding energy of the parent nucleus:
$Q = E_{b2} - E_{b1}$
$Q = 2040 \,MeV - 1824 \,MeV = 216 \,MeV$
$E_{b1} = 240 \times 7.6 \,MeV = 1824 \,MeV$
The binding energy of the two daughter fragments,each with $A = 120$,is given by:
$E_{b2} = 2 \times (120 \times 8.5 \,MeV) = 2 \times 1020 \,MeV = 2040 \,MeV$
The energy released in the process is the difference between the total binding energy of the products and the binding energy of the parent nucleus:
$Q = E_{b2} - E_{b1}$
$Q = 2040 \,MeV - 1824 \,MeV = 216 \,MeV$
Explore More
Similar Questions
The energy released in a typical nuclear fusion reaction is approximately..........$MeV$.
Under certain circumstances,a nucleus can decay by emitting a particle more massive than an $\alpha$-particle. Consider the following decay processes:
$_{88}^{223} Ra \rightarrow _{82}^{209} Pb + _{6}^{14} C$
$_{88}^{223} Ra \rightarrow _{86}^{219} Rn + _{2}^{4} He$
Calculate the $Q$-values for these decays and determine that both are energetically allowed.
$_{88}^{223} Ra \rightarrow _{82}^{209} Pb + _{6}^{14} C$
$_{88}^{223} Ra \rightarrow _{86}^{219} Rn + _{2}^{4} He$
Calculate the $Q$-values for these decays and determine that both are energetically allowed.
Medium
View SolutionThe energy released per fission of uranium-$235$ is about $200 \, MeV$. $A$ reactor using $U-235$ as fuel is producing $1000 \, kW$ power. The number of $U-235$ nuclei undergoing fission per second is approximately:
Difficult
View SolutionThe graph of binding energy per nucleon $(BE/A)$ versus mass number $(A)$ is shown in the figure. Which of the following options is correct?
Medium
View SolutionAssertion : Energy is released in nuclear fission.
Reason : Total binding energy of the fission fragments is larger than the total binding energy of the parent nucleus.
Reason : Total binding energy of the fission fragments is larger than the total binding energy of the parent nucleus.
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo