A nucleus X emits a $$\beta $$-particle to produce a nucleus Y. If their atomic masses are M_x and M_y respectively, then the maximum energy of the $$\beta $$-particle emitted is (where, m_e is the mass of an electron and c is the velocity of light)

For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV, respectively. If a nucleus of mass number 238 breaks into two nuclei of nearly equal masses, what will be the approximate amount of energy released in the process of fission?

A parent nucleus X undergoes $$\alpha$$-decay with a half-life of 75000 yrs. The daughter nucleus Y undergoes $$\beta$$-decay with a half-life of 9 months. In a particular sample, it is found that the rate of emission of $$\beta$$-particles is nearly constant (over several months) at $${10^7}/h$$. What will be the number of $$\alpha$$-particles emitted in an hour?

A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2000 times heavier than an electron, what will be the relation between the de Broglie wavelength of the proton ($$\lambda$$_p) and that of electron ($$\lambda$$_e)?