Question 341:
easyThe power obtained in a reactor using $ U^{235} $ disintegration is 1000 kW. The mass decay of $ U^{235} $ per hour is:
(2011 Pre)
Power $ P = 1000 $ kW $ = 10^6 $ J/s. Energy produced in one hour $ E = 10^6 \times 3600 = 3.6 \times 10^9 $ J. Using $ E = mc^2 $, mass decay $ m = E / c^2 = (3.6 \times 10^9) / (3 \times 10^8)^2 = 4 \times 10^{-8} $ kg = 40 micrograms.
Question 342:
easyThe binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is:
(2010 Mains)
Binding energy of two deuterium nuclei = $ 2 \times (2 \times 1.1) = 4.4 $ MeV. Binding energy of the helium nucleus = $ 4 \times 7.0 = 28.0 $ MeV. Energy released = Final BE - Initial BE = $ 28.0 - 4.4 = 23.6 $ MeV.
Question 343:
easyThe mass of a $ _3^7Li $ nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of $ _3^7Li $ nucleus is nearly:
(2010 Pre)
Mass defect $ \Delta m = 0.042 $ u. Total binding energy $ = \Delta m \times 931.5 $ MeV = $ 0.042 \times 931.5 = 39.123 $ MeV. Binding energy per nucleon = $ 39.123 / 7 \approx 5.6 $ MeV.
Question 344:
easy$ M_p $ denotes the mass of a proton and $ M_n $ that of a neutron. A given nucleus, of binding energy B, contains Z protons and N neutrons. The mass M(N, Z) of the nucleus is given by (c is velocity of light):
(2004)
The binding energy B is given by $ B = [Z M_p + N M_n - M(N, Z)] c^2 $. Rearranging for the mass of the nucleus gives $ M(N, Z) = Z M_p + N M_n - B/c^2 $.
Question 345:
easyThe mass of proton is 1.0073 u and that of neutron is 1.0087 u (u = atomic mass unit). The binding energy of $ _2^4He $ is (Given: helium nucleus mass $ \approx 4.0015 $ u)
(2003)
Mass of constituents = $ 2(1.0073) + 2(1.0087) = 4.0320 $ u. Mass defect $ \Delta m = 4.0320 - 4.0015 = 0.0305 $ u. Binding energy $ = 0.0305 \times 931.5 $ MeV $ \approx 28.4 $ MeV.
Question 346:
easy$ M_n $ and $ M_p $ represent the mass of neutron and proton respectively. An element having mass M has N neutron and Z-protons, then the correct relation will be:
(2001)
Due to the mass defect associated with the binding energy of the nucleus, the actual mass of the nucleus (M) is always less than the sum of the individual masses of its constituent nucleons ($ N M_n + Z M_p $).
Question 347:
easyThe binding energy per nucleon is maximum in case of
(1993)
The binding energy per nucleon curve peaks around mass number A = 56. Thus, $ _{26}^{56}Fe $ has the maximum binding energy per nucleon, which is approximately 8.8 MeV.
Question 348:
easyThe energy equivalent of one atomic mass unit is
(1992)
By Einstein's mass-energy equivalence $ E = mc^2 $, a mass of 1 atomic mass unit (1 u) is equivalent to approximately 931.5 MeV of energy.
Question 349:
easyThe mass of $ \alpha $-particle is
(1992)
An alpha particle is a helium nucleus consisting of two protons and two neutrons. Due to the mass defect which provides its binding energy, its total mass is less than the sum of the masses of its constituent individual nucleons.
Question 350:
easyIf the nuclear force between two protons, two neutrons and between proton and neutron is denoted by $ F_{pp} $, $ F_{nn} $ and $ F_{pn} $ respectively, then
(1990)
The strong nuclear force is charge-independent. Therefore, the strong interaction is identical for proton-proton, neutron-neutron, and proton-neutron pairs, rendering them approximately equal ($ F_{pp} \approx F_{nn} \approx F_{pn} $) when ignoring minor Coulombic repulsion.