Question 131:
easyWhen an electron do transition from $n = 4$ to $n = 2$, then emitted line in spectrum will be:
(2000)
Transitions ending at $n=2$ belong to the Balmer series. The transition $n=3 \rightarrow 2$ is the first line, and $n=4 \rightarrow 2$ is the second line of the Balmer series.
Question 132:
easyIn the Bohr model of H-atom, an electron (e) is revolving around a proton (p) with velocity v, if r is the radius of orbit and m is mass and $\epsilon_0$ is vacuum permittivity, the value of v is:
(1998)
The necessary centripetal force is provided by the electrostatic force of attraction. Thus, $\frac{mv^2}{r} = \frac{1}{4\pi\epsilon_0} \frac{e^2}{r^2}$. Solving for velocity yields $v = \frac{e}{\sqrt{4\pi\epsilon_0 m r}}$.
Question 133:
easyThe energy of the ground electronic state of hydrogen atom is $-13.6 eV$. The energy of the first excited state will be
(1997)
The energy of the nth state is given by $E_n = \frac{-13.6}{n^2} eV$. The first excited state corresponds to $n=2$. Therefore, $E_2 = \frac{-13.6}{2^2} = -3.4 eV$.
Question 134:
easyWhen hydrogen atom is in its first excited level, its radius is of the Bohr radius.
(1997)
The radius of the nth Bohr orbit is $r_n = r_0 n^2$, where $r_0$ is the Bohr radius. For the first excited level ($n=2$), $r_2 = r_0(2^2) = 4r_0$. Hence, it is 4 times the Bohr radius.
Question 135:
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 136:
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 137:
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 138:
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 139:
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 140:
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 $R_1 / R_2 = (1/2)^{1/3} = 1 : 2^{1/3}$.