The energy released in nuclear reactions is produced by a ch

The energy released in nuclear reactions is produced by a change in mass between the initial and final particles. In one of the possible alpha decays an isotope of uranium with m = 232.03714 u (atomic mass unit u = 1.6605 times 10^-27 kg) decays to an isotope of thorium with m = 228.02873 u plus an alpha particle with m = 4.00260 u. Find out the energy released in this fission reaction in Joules_________ and in MeV__________. Assume that all participating particle are practically at rest. In your calculations use many significant figures. What is the speed of a relativistic electron whose E_total is 1.536 MeV?___________ Electron\'s rest mass is 9.11 times 10^-31 kg. The work functions for iron (Fe), sodium (Na), copper (Cu), and cesium (Cs) are 4.5, 2.3,4.7, and 2.1 eV respectively. Which of these metals will exhibit photoelectric effect when white light (400 to 700 nm) shines on them?__________ What is the energy, frequency, and wavelength of the photons that could cause an electronic transition in a hydrogen atom (a) from the n = 3 state to the n = 5 state?____________, from the n = 1 state to n = infinity state? (this process is called \"ionization\")__. Calculate the de Broglie wavelength of a proton that has a kinetic energy of 10 eV____________.

Solution

(1).mass of uranium m = 232.03714 u

mass of thorium m \' = 228.02873 u

mass of alpha particle m \" = 4.00260 u

mass defect dm = m - m\' -m \"

                        = 232.03714 u - 228.02873 u-4.00260 u

                        = 5.81 x10 ^-3 u

                        = 5.81x10 ^-3 x1.6605 x10 ^-27 kg

Energy released E = dm c ²

                           = (5.81 x10 ^-3 )(1.6605 x10 ^-27 )(3 x10 ⁸ ) ²

                          = 8.682 x10 ^-13 J

                         =[(8.682 x10 ^-13 )/(1.6 x10 ^-13)] MeV

                         = 5.426 MeV