364057
Consider a nuclear reaction in which the target particle is \({}_9{F^{19}}\) and it is at rest initially. A fast moving neutron \({}_0{n^1}\) collides with \({}_9{F^{19}}.\) If \(Q\) value of the reaction is \(4\,MeV\) then find the threshold energy of the neutron.
1 \(2.0\,MeV\)
2 \(8.0\,MeV\)
3 \(4.0\,MeV\)
4 \(4.2\,MeV\)
Explanation:
\({E_{Th}} = Q\left[ {1 + \frac{m}{M}} \right]\) we can approximate that \(m = {m_n} = 1\;amu\) \(M = {m_F} = 19\;amu\) Given that \(Q = 4MeV\) \({E_{Th}} = 4MeV\left[ {1 + \frac{1}{{19}}} \right] = 4.2MeV\)
PHXII13:NUCLEI
364058
Consider a nuclear reaction with target particle at rest and its mass is \(M\). The mass of moving particle is m and velocity is \(u\). The energy required for the reaction to take place is \(Q\). Find the threshold energy of the particle of mass \(m\).
1 \(Q\left[ {1 + \frac{M}{m}} \right]\)
2 \(Q\left[ {M + m} \right]\)
3 \(Q\left[ {1 + \frac{m}{M}} \right]\)
4 \(\frac{{Qm}}{M}\)
Explanation:
For the requirement of least \(K\).\(E\) (Threshold energy) the nature of collision is inelastic. From consevation of linear momentum \(mu + M(0) = (m + M)v\,\,\,\,\,\,(1)\) From conservation of energy \(\frac{1}{2}mu = \frac{1}{2}(m + M){v^2} + Q\,\,\,\,(2)\) Where \(Q\) is the energy required for nuclear reaction which has to come from \(K\).\(E\) of the incoming particle. From (1) & (2) \(\frac{1}{2}m{u^2} = \frac{1}{2}(m + M)\frac{{{m^2}{u^2}}}{{{{(m + M)}^2}}} + Q\) \(\frac{1}{2}m{u^2} = \frac{1}{2}\frac{{{m^2}{u^2}}}{{(m + M)}} + Q\) \(\frac{1}{2}m{u^2}\left[ {1 - \frac{m}{{m + M}}} \right] = Q\) \({E_{Th}} = Q\left[ {1 + \frac{m}{M}} \right]\) \(\left( {\frac{1}{2}m{u^2} = {E_{Th}}} \right)\)
PHXII13:NUCLEI
364059
Consider a nuclear reaction with target particle of mass \(2m\) which is present at rest. The mass of moving particle is \(m\). The energy required for the reaction to take place is \(4MeV\). If the moving particle carries an energy of \(5MeV\) then the nature of collision is
1 Elastic
2 Inelastic
3 Partially elastic
4 Information is insufficient.
Explanation:
\({E_{Th}} = Q\left[ {1 + \frac{m}{{2m}}} \right] = 4\left[ {\frac{3}{2}} \right]\) \({E_{Th}} = 6MeV\) As \(E = 5\,MeV\) so reaction does not take place and the collision is elastic, since the \(K\).\(E\) of system does not convert into another form.
364057
Consider a nuclear reaction in which the target particle is \({}_9{F^{19}}\) and it is at rest initially. A fast moving neutron \({}_0{n^1}\) collides with \({}_9{F^{19}}.\) If \(Q\) value of the reaction is \(4\,MeV\) then find the threshold energy of the neutron.
1 \(2.0\,MeV\)
2 \(8.0\,MeV\)
3 \(4.0\,MeV\)
4 \(4.2\,MeV\)
Explanation:
\({E_{Th}} = Q\left[ {1 + \frac{m}{M}} \right]\) we can approximate that \(m = {m_n} = 1\;amu\) \(M = {m_F} = 19\;amu\) Given that \(Q = 4MeV\) \({E_{Th}} = 4MeV\left[ {1 + \frac{1}{{19}}} \right] = 4.2MeV\)
PHXII13:NUCLEI
364058
Consider a nuclear reaction with target particle at rest and its mass is \(M\). The mass of moving particle is m and velocity is \(u\). The energy required for the reaction to take place is \(Q\). Find the threshold energy of the particle of mass \(m\).
1 \(Q\left[ {1 + \frac{M}{m}} \right]\)
2 \(Q\left[ {M + m} \right]\)
3 \(Q\left[ {1 + \frac{m}{M}} \right]\)
4 \(\frac{{Qm}}{M}\)
Explanation:
For the requirement of least \(K\).\(E\) (Threshold energy) the nature of collision is inelastic. From consevation of linear momentum \(mu + M(0) = (m + M)v\,\,\,\,\,\,(1)\) From conservation of energy \(\frac{1}{2}mu = \frac{1}{2}(m + M){v^2} + Q\,\,\,\,(2)\) Where \(Q\) is the energy required for nuclear reaction which has to come from \(K\).\(E\) of the incoming particle. From (1) & (2) \(\frac{1}{2}m{u^2} = \frac{1}{2}(m + M)\frac{{{m^2}{u^2}}}{{{{(m + M)}^2}}} + Q\) \(\frac{1}{2}m{u^2} = \frac{1}{2}\frac{{{m^2}{u^2}}}{{(m + M)}} + Q\) \(\frac{1}{2}m{u^2}\left[ {1 - \frac{m}{{m + M}}} \right] = Q\) \({E_{Th}} = Q\left[ {1 + \frac{m}{M}} \right]\) \(\left( {\frac{1}{2}m{u^2} = {E_{Th}}} \right)\)
PHXII13:NUCLEI
364059
Consider a nuclear reaction with target particle of mass \(2m\) which is present at rest. The mass of moving particle is \(m\). The energy required for the reaction to take place is \(4MeV\). If the moving particle carries an energy of \(5MeV\) then the nature of collision is
1 Elastic
2 Inelastic
3 Partially elastic
4 Information is insufficient.
Explanation:
\({E_{Th}} = Q\left[ {1 + \frac{m}{{2m}}} \right] = 4\left[ {\frac{3}{2}} \right]\) \({E_{Th}} = 6MeV\) As \(E = 5\,MeV\) so reaction does not take place and the collision is elastic, since the \(K\).\(E\) of system does not convert into another form.
364057
Consider a nuclear reaction in which the target particle is \({}_9{F^{19}}\) and it is at rest initially. A fast moving neutron \({}_0{n^1}\) collides with \({}_9{F^{19}}.\) If \(Q\) value of the reaction is \(4\,MeV\) then find the threshold energy of the neutron.
1 \(2.0\,MeV\)
2 \(8.0\,MeV\)
3 \(4.0\,MeV\)
4 \(4.2\,MeV\)
Explanation:
\({E_{Th}} = Q\left[ {1 + \frac{m}{M}} \right]\) we can approximate that \(m = {m_n} = 1\;amu\) \(M = {m_F} = 19\;amu\) Given that \(Q = 4MeV\) \({E_{Th}} = 4MeV\left[ {1 + \frac{1}{{19}}} \right] = 4.2MeV\)
PHXII13:NUCLEI
364058
Consider a nuclear reaction with target particle at rest and its mass is \(M\). The mass of moving particle is m and velocity is \(u\). The energy required for the reaction to take place is \(Q\). Find the threshold energy of the particle of mass \(m\).
1 \(Q\left[ {1 + \frac{M}{m}} \right]\)
2 \(Q\left[ {M + m} \right]\)
3 \(Q\left[ {1 + \frac{m}{M}} \right]\)
4 \(\frac{{Qm}}{M}\)
Explanation:
For the requirement of least \(K\).\(E\) (Threshold energy) the nature of collision is inelastic. From consevation of linear momentum \(mu + M(0) = (m + M)v\,\,\,\,\,\,(1)\) From conservation of energy \(\frac{1}{2}mu = \frac{1}{2}(m + M){v^2} + Q\,\,\,\,(2)\) Where \(Q\) is the energy required for nuclear reaction which has to come from \(K\).\(E\) of the incoming particle. From (1) & (2) \(\frac{1}{2}m{u^2} = \frac{1}{2}(m + M)\frac{{{m^2}{u^2}}}{{{{(m + M)}^2}}} + Q\) \(\frac{1}{2}m{u^2} = \frac{1}{2}\frac{{{m^2}{u^2}}}{{(m + M)}} + Q\) \(\frac{1}{2}m{u^2}\left[ {1 - \frac{m}{{m + M}}} \right] = Q\) \({E_{Th}} = Q\left[ {1 + \frac{m}{M}} \right]\) \(\left( {\frac{1}{2}m{u^2} = {E_{Th}}} \right)\)
PHXII13:NUCLEI
364059
Consider a nuclear reaction with target particle of mass \(2m\) which is present at rest. The mass of moving particle is \(m\). The energy required for the reaction to take place is \(4MeV\). If the moving particle carries an energy of \(5MeV\) then the nature of collision is
1 Elastic
2 Inelastic
3 Partially elastic
4 Information is insufficient.
Explanation:
\({E_{Th}} = Q\left[ {1 + \frac{m}{{2m}}} \right] = 4\left[ {\frac{3}{2}} \right]\) \({E_{Th}} = 6MeV\) As \(E = 5\,MeV\) so reaction does not take place and the collision is elastic, since the \(K\).\(E\) of system does not convert into another form.
