Question 101:
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 102:
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 103:
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 104:
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 105:
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.
Question 106:
easyWhich of the following statements is true for nuclear forces?
(1990)
Nuclear forces are the strongest forces in nature but they are strictly short-range forces, operating effectively only over distances of about 2 to 3 femtometers (fm). They do not follow the inverse square law.
Question 107:
easyThe average binding energy of a nucleon inside an atomic nucleus is about
(1989)
For most stable nuclei with intermediate mass numbers (30 < A < 170), the average binding energy per nucleon is approximately 8 MeV.
Question 108:
easyA radio isotope $X$ with a half life of $1.4 \times 10^9$ years decays to $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$ in the ratio $1 : 7$. The age of the rock is:
(2014)
Ratio $X/Y = 1/7$ implies $X/(X+Y) = 1/8 = (1/2)^3$. Thus, 3 half-lives have elapsed. The age of the rock is $3 \times 1.4 \times 10^9 = 4.2 \times 10^9$ years.
Question 109:
easyThe half life of a radioactive isotope ‘$X$’ is 20 years. It decays to another element ‘$Y$’ which is stable. The two elements ‘$X$’ and ‘$Y$’ were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be:
(2013)
The fraction of remaining radioactive isotope is $X/(X+Y) = 1/(1+7) = 1/8 = (1/2)^3$. Three half-lives have passed, so age $t = 3 \times 20 = 60$ years.
Question 110:
easyThe half life of a radioactive nucleus is 50 days. The time interval $(t_2 – t_1)$ between the time $t_2$ when 2 / 3 of it has decayed and the time $t_1$ when 1 / 3 of it had decayed is:
(2012 Mains)
At $t_1$, fraction remaining is $1 - 1/3 = 2/3$. At $t_2$, fraction remaining is $1 - 2/3 = 1/3$. The ratio of remaining nuclei is $(1/3)/(2/3) = 1/2$. This represents exactly one half-life, which is 50 days.