Neco Model Questions Vol1 2017 Physics Question 48

The nuclear fission reaction \[\,_{92}^{238}\text{U}+\,_{0}^{1}\text{n}\rightarrow\,_{56}^{141}\text{Ba}+\,_{36}^{95}\text{Kr}+3\,_{0}^{1}\text{n}\,\] occurs with the following atomic masses (in atomic mass units): \(m(\,_{92}^{238}\text{U})=238.050788\), \(m(\,_{0}^{1}\text{n})=1.008665\), \(m(\,_{56}^{141}\text{Ba})=140.914411\), \(m(\,_{36}^{95}\text{Kr})=94.931910\).\ (a) Calculate the Q‑value of the reaction in MeV (to three significant figures).\ (b) Using the Coulomb‑barrier approximation \(E_{C}=\dfrac{Z_{1}Z_{2}e^{2}}{4\pi\varepsilon_{0}r}\) with \(e^{2}/(4\pi\varepsilon_{0})=1.44\ \text{MeV·fm}\) and \(r=1.2\ \text{fm}\bigl(A_{1}^{1/3}+A_{2}^{1/3}\bigr)\), determine whether the released energy is sufficient to overcome the Coulomb barrier between the two fission fragments (Ba and Kr). Give the barrier energy (in MeV, to the nearest whole number) and a brief conclusion.