Question 321:
easyThe energy of a hydrogen atom in its ground state is $-13.6 eV$. The energy of the level corresponding to the quantum number $n = 2$ in the hydrogen atom is
(1996)
The energy of an electron in the nth orbit is $E_n = \frac{-13.6}{n^2} eV$. For $n=2$, the energy is $E_2 = \frac{-13.6}{4} = -3.4 eV$.
Question 322:
easyA nucleus represented by the symbol $^{A}_{Z}X$ has:
(2004)
In standard nuclear notation $^{A}_{Z}X$, Z represents the atomic number (number of protons) and A represents the mass number (total number of protons and neutrons). Hence, the number of neutrons is $A - Z$.
Question 323:
easyThe mass number of a nucleus is:
(2003)
Mass number A is the sum of protons and neutrons, while atomic number Z is just the number of protons. For hydrogen ($^1H$), there are no neutrons, so A = Z. For all other stable nuclei, A > Z. Thus, it is sometimes equal.
Question 324:
easyThe volume occupied by an atom is greater than the volume of the nucleus by a factor of about:
(2003)
The radius of an atom is of the order of $10^{-10} m$, and the radius of a nucleus is of the order of $10^{-15} m$. The ratio of their volumes is proportional to the cube of their radii ratio: $(10^{-10} / 10^{-15})^3 = (10^5)^3 = 10^{15}$.
Question 325:
easyBoron has two isotopes $^{10}_{5}B$ and $^{11}_{5}B$. If atomic weight of Boron is 10.81 then ratio of $^{10}_{5}B$ to $^{11}_{5}B$ in nature will be:
(1998)
Let the fractional abundance of $^{10}B$ be $x$ and $^{11}B$ be $1-x$. The atomic weight is $10x + 11(1-x) = 10.81$. Solving this yields $11 - x = 10.81$, so $x = 0.19$. The ratio is $0.19 : 0.81 = 19 : 81$.
Question 326:
easyA nucleus ruptures into two nuclear parts, which have their velocity ratio equal to 2 : 1. What will be the ratio of their nuclear size (nuclear radius)?
(1996)
By conservation of momentum, $m_1 v_1 = m_2 v_2$, meaning the mass ratio is $m_1 / m_2 = v_2 / v_1 = 1 / 2$. Since radius $R \propto m^{1/3}$, the ratio of their radii is $R_1 / R_2 = (1/2)^{1/3} = 1 : 2^{1/3}$.
Question 327:
easyThe mass number of He is 4 and that of sulphur is 32. The radius of sulphur nucleus is larger than that of helium by the factor of
(1995)
The radius of a nucleus is proportional to the cube root of its mass number ($R \propto A^{1/3}$). The ratio $R_S / R_{He} = (32 / 4)^{1/3} = (8)^{1/3} = 2$. Therefore, the radius is larger by a factor of 2.
Question 328:
easyThe mass density of a nucleus varies with mass number A as
(1992)
Nuclear density is defined as mass per unit volume. Since mass is proportional to A and volume is proportional to $R^3 \propto A$, the density is proportional to $A/A = 1$. It is a constant independent of A.
Question 329:
easyThe constituents of atomic nuclei are believed to be
(1991)
According to the universally accepted proton-neutron model of the nucleus, atomic nuclei are composed of protons and neutrons, which are collectively referred to as nucleons.
Question 330:
easyA nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is :
(2022)
The radius of a nucleus is related to its mass number by $R = R_0 A^{1/3}$. The ratio of their radii is $R_1 / R_2 = (A_1 / A_2)^{1/3} = (125 / 64)^{1/3}$. This gives $R_1 / R_2 = 5 / 4$, so the ratio is $5 : 4$.