A nucleus of mass 20 u emits a gamma phot | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given: Mass of nucleus $ M = 20 u = 20 	imes 1.6 	imes 10^{-27} kg = 3.2 	imes 10^{-26} kg $.Energy of photon $ E = 6 MeV = 6 	imes 10^6 eV =

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given: Mass of nucleus $ M = 20 u = 20 	imes 1.6 	imes 10^{-27} kg = 3.2 	imes 10^{-26} kg $.Energy of photon $ E = 6 MeV = 6 	imes 10^6 eV = 6 	imes 10^6 	imes 1.6 	imes 10^{-19} J = 9.6 	imes 10^{-13} J $.By conservation of linear momentum, the momentum of the nucleus $ p_n $ must be equal to the momentum of the photon $ p_p $.$ p_p = \frac{E}{c} = \frac{9.6 	imes 10^{-13} J}{3 	imes 10^8 m/s} = 3.2 	imes 10^{-21} kg \cdot m/s $.Since $ p_n = p_p $, the kinetic energy of the nucleus $ K_n $ is given by $ K_n = \frac{p_n^2}{2M} $.$ K_n = \frac{(3.2 	imes 10^{-21})^2}{2 	imes 3.2 	imes 10^{-26}} = \frac{10.24 	imes 10^{-42}}{6.4 	imes 10^{-26}} = 1.6 	imes 10^{-16} J $.Converting to $ eV $: $ K_n = \frac{1.6 	imes 10^{-16} J}{1.6 	imes 10^{-19} J/eV} = 10^3 eV = 1 keV $.Thus, the kinetic energy of the nucleus is $ 1 keV $.

$A$ nucleus of mass $ 20 u $ emits a $ \gamma $ photon of energy $ 6 MeV $. If the emission is assumed to occur when the nucleus is free and at rest, then the nucleus will have a kinetic energy nearest to (take $ 1 u = 1.6 \times 10^{-27} kg $): (in $keV$)

Similar Questions

If the binding energy per nucleon for $\,_3^7\,Li\,\,$ and $\,_2^4\,\,He$ are $5.60 \,MeV$ and $7.06 \,MeV$ respectively, then the energy of the proton in the reaction $p\,\, + \,\,_3^7\,\,Li\,\, \to \,\,2\,_2^4\,\,He$ must be .......... $MeV$.

The binding energy of a nucleon in a nucleus is of the order of a few

The mass and energy equivalent to $1\, a.m.u.$ are respectively:

The binding energy per nucleon for $_8O^{16}$ and $_8O^{17}$ are $7.97 \, MeV$ and $7.75 \, MeV$ respectively. The energy required to remove a neutron from $_8O^{17}$ is (in $MeV$):

The mass of a proton is $1.0073 \; u$ and that of a neutron is $1.0087 \; u$ ($u =$ atomic mass unit). The binding energy of ${ }_2^4 \text{He}$ is (Given: helium nucleus mass $\approx 4.0015 \; u$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module