Additional Questions - Chapter 8 Atomic and Nuclear Physics 12th Science Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

AdditionalQuestions
Multiple Choice Questions
Question 1.
The potential difference applied to an $\mathrm{X}$-ray tube is $5 \mathrm{kV}$ and the current through it is 3.2 $\mathrm{mA}$. Then the number of electrons striking the target per second is
(a) $2 \times 10^{16}$
(b) $5 \times 10^{18}$
(c) $1 \times 10^{17}$
(d) $4 \times 10^5$
Answer:
(a) $2 \times 10^{16}$
Hint:
$
\mathrm{n}=\frac{I t}{e}=\frac{3.2 \times 10^{-3} \times 1}{1.6 \times 10^{-19}}=2 \times 10^{16}
$
Question 2.
The allowed energy for the particle for a particular value of $\mathrm{n}$ is proportional to
(a) $\mathrm{a}^{-2}$
(b) $\mathrm{a}^{-3 / 2}$
(c) $\mathrm{a}^{-1}$
(d) $\mathrm{a}^2$
Answer:
(a) $\mathrm{a}^{-2}$
Hint:
For the standing wave, $\mathrm{a}=\mathrm{n} \frac{\lambda}{2}$ or $\lambda=\frac{2 a}{n}$
$
\mathrm{P}=\frac{h}{\lambda}=\frac{n h}{2 a} ; \mathrm{E}=\frac{p^2}{2 m}=\frac{n^2 h^2}{2 a^2 m} ; \mathrm{E} \propto \mathrm{a}^{-2}
$

Question 3.
A diatomic molecular has moment of inertia I. By Bohr's quantization condition its rotational energy in the $\mathrm{n}^{\text {th }}$ level ( $\mathrm{n}=0$ is not allowed) is
(a) $\frac{1}{n^2}\left(\frac{h^2}{8 \pi^2 \mathrm{I}}\right)$
(b) $\frac{1}{n}\left(\frac{h^2}{8 \pi^2 \mathrm{I}}\right)$
(c) $n\left(\frac{h^2}{8 \pi^2 I}\right)$
(d) $n^2\left(\frac{h^2}{8 \pi^2 I}\right)$
Answer:
(d) $n^2\left(\frac{h^2}{8 \pi^2 I}\right)$
Hint:
Angular momentum, $\mathrm{L}=\frac{n h}{2 \pi}$
Rotation K.E $=\frac{L^2}{2 I}=\frac{n^2 h^2}{8 \pi^2 I}$.
Question 4.
The speed of the particle, that can take discrete values is proportional to
(a) $\mathrm{n}^{-3 / 2}$
(b) $\mathrm{n}^{-1}$
(c) $\mathrm{n}^{1 / 2}$
(d) $\mathrm{n}$
Answer:
(d) $\mathrm{n}$
Hint:
$
\mathrm{P}=\mathrm{mv}=\frac{n h}{2 a} ; \mathrm{V} \propto \mathrm{n}
$
Question 5.
If $13.6 \mathrm{eV}$ energy is required to 10 is the hydrogen atom, then energy required to remove an electron from $\mathrm{n}=2$ is
(a) $10.2 \mathrm{eV}$

(b) $0 \mathrm{eV}$
(c) $3.4 \mathrm{eV}$
(d) $6.8 \mathrm{eV}$
Answer:
(c) $3.4 \mathrm{eV}$
Hint:
$
\begin{aligned}
& \mathrm{E}_{\mathrm{n}}=\frac{13.6^2}{n} \mathrm{eV} \\
& \therefore \Delta \mathrm{E}=\mathrm{E}_{\propto}-\mathrm{E}_2=0+\frac{13.6^2}{n}=3.4 \mathrm{eV} .
\end{aligned}
$
Question 6.
Which of the following transitions in hydrogen atoms emits photon of highest frequency?
(a) $\mathrm{n}=1$ to $\mathrm{n}=2$
(b) $\mathrm{n}=2$ to $\mathrm{n}=6$
(c) $\mathrm{n}=6$ to $\mathrm{n}=2$
(d) $\mathrm{n}=2$ to $\mathrm{n}=1$
Answer:
(d) $\mathrm{n}=2$ to $\mathrm{n}=1$
Hint:
The energy difference $E_2-E_1$ is maximum as calculated in the above problem.
Question 7.
The wavelengths involved in the spectrum of deuterium ${ }_1^2 H$ are slightly different from that of hydrogen spectrum because
(a) sizes of the two nuclei are different
(b) masses of the two nuclei are different
(c) attraction between the electron and the nucleus is different in the two cases
(d) nuclear forces are different in the two cases
Answer:
(b) masses of the two nuclei are different
Hint:
It is because the masses of the two nuclei are different.

Question 8.
Energy required for the electron excitation in $\mathrm{Li}^{++}$from the first to the third Bohr orbit is
(a) $12.1 \mathrm{eV}$
(b) $36.3 \mathrm{eV}$
(b) $36.3 \mathrm{eV}$
(c) $108.8 \mathrm{eV}$
Answer:
(c) $108.8 \mathrm{eV}$
Hint:
$
\mathrm{E}_{\mathrm{n}}=-13.6 \frac{Z^2}{n^2}
$
$
\begin{aligned}
& \Delta \mathrm{E}=\mathrm{E}_3-\mathrm{E}_2=13.6(3)^2\left[\frac{1}{1^2}-\frac{1}{3^2}\right] \\
& =\frac{13.6 \times 9 \times 8}{9}=108.8 \mathrm{eV} .
\end{aligned}
$
Question 9.
Minimum energy required to take out the only one electron from ground state of $\mathrm{He}^{+}$is
(a) $13.6 \mathrm{eV}$
(b) $54.4 \mathrm{eV}$
(c) $27.2 \mathrm{eV}$
(d) $6.8 \mathrm{eV}$
Answer:
(b) $54.4 \mathrm{eV}$
Hint:
Ionisation energy, $\mathrm{E}=13.6 \mathrm{Z}^2 \mathrm{eV}$
$\mathrm{Fe} \mathrm{He}^{+}, \mathrm{Z}=2$
$
\therefore \mathrm{E}=13.6 \times(2)^2=13.6 \times 4=54.4 \mathrm{eV} \text {. }
$

Question 10.
Energy of characteristic X-ray is a consequence of
(a) energy of projectile electron
(b) thermal energy of target
(c) transition in target atoms
(d) none of the above
Answer:
(c) transition in target atoms.
Question 11.
How much energy is needed to excite an electron in $\mathrm{H}$-atom from ground state to first excited state?
(a) $-13.6 \mathrm{eV}$
(b) $-10.2 \mathrm{eV}$
(c) $+10.2 \mathrm{eV}$
(d) $+13.6 \mathrm{eV}$
Answer:
(c) $+10.2 \mathrm{eV}$
Hint:
$\mathrm{E}_1=-13.6 \mathrm{eV}$
$\mathrm{E}_2=-13.6 / 22^2=-3.4 \mathrm{eV}$
Required excitation energy
$
=\mathrm{E}_2-\mathrm{E}_2=-3.4+13.6=+10.2 \mathrm{eV} \text {. }
$
Question 12.
For an electron in the second orbit of hydrogen, what is the moment of momentum as per the Bohr's model?
(a) $2 \pi \mathrm{h}$
(b) $\pi \mathrm{h}$
(c) $\mathrm{h} / \pi$
(d) $2 \mathrm{~h} / \pi$
Answer:
(c) $\mathrm{h} / \pi$
Hint:
In second orbit of hydrogen, $\mathrm{L}=2\left(\frac{h}{2 \pi}\right)=\frac{h}{\pi}$.
Question 13.
The total energy of an electron in the first excited state of hydrogen atom is about $-3.4 \mathrm{eV}$. Its kinetic energy in this state is
(a) $3.4 \mathrm{eV}$
(b) $6.8 \mathrm{eV}$
(c) $-3.4 \mathrm{eV}$
(d) $-6.8 \mathrm{eV}$
Answer:
(a) $3.4 \mathrm{eV}$
Hint:
$\mathrm{K} . \mathrm{E}=-$ Total energy $=+3.4 \mathrm{eV}$.
Question 14.
The energy of the ground electronic state of hydrogen atom is $13.6 \mathrm{eV}$. The energy of the first excited state will be
(a) $-27.2 \mathrm{eV}$
(b) $-52.4 \mathrm{eV}$
(c) $-3.4 \mathrm{eV}$
(d) $-6.8 \mathrm{eV}$
Answer:
(c) $-3.4 \mathrm{eV}$
Hint:
For the first excited state, $\mathrm{n}=2$
$
\therefore \mathrm{E}_2=\frac{E_1}{E_2}=\frac{-13.6 \mathrm{eV}}{4}=-3.4 \mathrm{eV} \text {. }
$

Question 15.
The total energy of electron in the ground state of hydrogen atom is $-13.6 \mathrm{eV}$. The kinetic energy of an electron in the first excited state is
(a) $6.8 \mathrm{eV}$
(b) $13.6 \mathrm{eV}$
(c) $1.7 \mathrm{eV}$
(d) $3.4 \mathrm{eV}$
Answer:
(d) $3.4 \mathrm{eV}$
Hint:
Total energy in the first excited state,
$
\begin{aligned}
& \mathrm{E}_2=\frac{E_1}{E_2}=\frac{E_1}{2^2}=\frac{-13.6}{4}=-3.4 \mathrm{eV} \\
& \mathrm{K} . \mathrm{E}=-\mathrm{E}_2=3.4 \mathrm{eV} .
\end{aligned}
$
Question 16.
Bohr's theory of hydrogen atom did not explain fully
(a) diameter of $\mathrm{H}$-atom
(b) emission spectra
(c) ionisation energy
(d) the fine structure of even hydrogen spectrum
Answer:
(d) the fine structure of even hydrogen spectrum
Hint:
Bohr theory could not explain the five structure of hydrogen spectrum.
Question 17.
In Bohr's model of an atom, which of the following is an integral multiple of $\frac{h}{2 \pi}$ ?
(a) Kinetic energy
(b) Radius of an atom
(c) Potential energy
(d) Angular momentum
Answer:
(d) Angular momentum

Hint:
$
\mathrm{L}=\mathrm{mvr}=\frac{n h}{2 \pi}
$
Question 18.
According to Bohr's theory, relation between $\mathrm{n}$ and radius of orbit is:
(a) $\mathrm{r} \propto \frac{1}{n}$
(b) $r \propto n$
(c) $r \propto n^2$
(d) $\mathrm{r} \propto \frac{1}{n^2}$
Answer:
(c) $r \propto n^2$
Hint:
$\mathrm{r}=\frac{n^2 h^2}{4 \pi^2 m K Z e^2}$ i.e., $\mathrm{r} \propto \mathrm{n}^2$.
Question 19.
In Bohr's model of hydrogen atom, the radius of the first electron orbit is $0.53 \AA$. What will
be the radius of the third orbit?
(a) $4.77 Å$
(b) $47.7 Å$
(c) $9 Å$
(d) $0.09 Å$
Answer:
(a) $4.77 Å$
Hint:
$
\mathrm{r}_3=(3)^2 \mathrm{r}^1=9 \times 0.53=4.77 \AA .
$

Question 20.
In Bohr model of hydrogen atom, which of the following is quantised?
(a) linear velocity of electron
(b) angular velocity of electron
(c) linear momentum of electron
(d) angular momentum of electron
Answer:
(d) angular momentum of electron.
Question 21.
In Bohr's model, the atomic radius of the first orbit is $r_0$. Then, the radius of the third orbit is
(a) $\mathrm{r}_0 / 9$
(b) $\mathrm{r}_0$
(c) $9 r_0$
(d) $3 r_0$
Answer:
(c) $9 r_0$
Hint:
$
\begin{aligned}
& \mathrm{r}_{\mathrm{n}}=\mathrm{r}_1 \mathrm{n}^2, \text { where } \mathrm{r}_1=\mathrm{r}_0 \\
& \therefore \mathrm{v}_3=\mathrm{r}_0(3)^2 9 \mathrm{r}_0
\end{aligned}
$
Question 22.
What is ratio of Bohr magneton to the nuclear magneton?
(a) $\frac{m_p}{m_e}$
(b) $\frac{m_p^2}{m_e^2}$
(c) 1
(d) $\frac{m_e}{m_p}$
Answer:
(a) $\frac{m_p}{m_e}$

Hint:
Bohr magneton, $\mu_{\mathrm{B}}=\frac{e h}{2 m_e}$
Nuclear magneton, $\mu_{\mathrm{N}}=\frac{e h}{2 m_p}$
$
\therefore \frac{\mu_B}{\mu_N}=\frac{m_p}{m_e} \text {. }
$
Question 23.
In terms of Bohr radius $\mathrm{a}_0$, the radius of the second Bohr orbit of a hydrogen atom is given by
(a) $4 \mathrm{a}_0$
(b) $8 \mathrm{a}_0$
(c) $\sqrt{ } 2 a_0$
(d) $2 \mathrm{a}_0$
Answer:
(a) $4 \mathrm{a}_0$
Hint:
$
\begin{aligned}
& \mathrm{r}_{\mathrm{n}}=\mathrm{r}_1 \mathrm{n}^2 \\
& \mathrm{r}_2=\mathrm{a}_0(2)^2=4 \mathrm{a}_0
\end{aligned}
$
Question 24.
If an a-particle collides head on with a nucleus, what is impact parameter?
(a) zero
(b) infinite
(c) $10^{-10} \mathrm{~m}$
(d) $10^{10} \mathrm{~m}$
Answer:
(a) zero
Question 25 .
One femtometre is equivalent to
(a) $10^{15} \mathrm{~m}$
(b) $10^{-15} \mathrm{~m}$
(c) $10^{-12} \mathrm{~m}$
(d) $10^{11} \mathrm{~m}$
Answer:

(b) $10^{-15} \mathrm{~m}$
Question 26.
Wavelength of $\mathrm{K}_\alpha$ line of $\mathrm{X}$-ray spectra varies with atomic number as
(a) $\lambda \propto Z$
(b) $\lambda \propto \sqrt{Z}$
(c) $\lambda \propto \frac{1}{Z^2}$
(d) $\lambda \propto \frac{1}{\sqrt{ } Z}$
Answer:
(c) $\lambda \propto \frac{1}{Z^2}$
Hint:
ccording to moseley's law, $\sqrt{ } \mathrm{V}=\mathrm{a}(\mathrm{Z}-\mathrm{b})$ or $\mathrm{V}=\frac{c}{\lambda}=\mathrm{a}^2(\mathrm{Z}-\mathrm{b})^2$
$\therefore$ (c) $\lambda \propto \frac{1}{Z^2}$.
Question 27.
The shortest wavelength of $\mathrm{X}$-rays, emitted from a X-ray tube, depend upon
(a) current in the tube
(b) voltage applied to the tube
(c) nature of glass material in the tube
(d) atomic number of the target material
Answer:
(b) voltage applied to the tube
Hint:
$
\lambda_{\min }=\frac{12375}{V(\text { volt })} Å; \lambda_{\min } \propto \frac{1}{V} \text {. }
$
Question 28.
During X-ray formation, if voltage is increased
(a) minimum wavelength decreases
(b) minimum wavelength increases
(c) intensity decreases
(d) intensity increases

Answer:
(a) minimum wavelength decreases
Hint:
As $\lambda_{\min } \propto \frac{1}{V}$ if voltage is increased, the minimum wavelength of X-rays emitted decreases.
Question 29.
What would be the radius of second orbit of $\mathrm{He}^{+}$ions?
(a) $1.058 Å$
(b) $3.023 Å$
(c) $2.068 Å$
(d) $4.458 Å$
Answer:
$1.058 Å$
Hint:
$
\mathrm{r}_{\mathrm{n}}=\frac{n^2}{Z} \mathrm{r}_1
$
For $\mathrm{He}^{+}$ion, $\mathrm{n}=2, \mathrm{Z}=2$
$
\therefore \mathrm{r}_2=\frac{4}{2} \times 0.59 Å=1.058 \AA \text {. }
$
Question 30.
The minimum wavelength of the X-rays produced by electrons accelerated through a potential difference of $\mathrm{V}$ volts is directly proportional to
(a) $\frac{1}{\sqrt{ } V}$
(b) $\frac{1}{V}$
(c) $\sqrt{ } \mathrm{V}$
(d) $\mathrm{V}^2$
Answer:
(b) $\frac{1}{V}$
Hint:
$\frac{h c}{\lambda}=\mathrm{eV}$ or $\lambda=\frac{h c}{e V}$, i.e., $\lambda \propto \frac{1}{V}$.

Question 31 .
Which source is associated with a line emission spectrum?
(a) Electric fire
(b) Neon street sign
(c) Red traffic light
(d) Sun
Answer:
(b) Neon street sign
Question 32.
Which one of the relation is correct between time period and number of orbits while an electron is revolving in a orbit?
(a) $\mathrm{T} \propto \frac{1}{n^2}$
(b) $T \propto n^2$
(c) $\mathrm{T} \propto \mathrm{n}^3$
(d) $\mathrm{T} \propto \frac{1}{n^2}$
Answer:
(c) $T \propto n^3$
Hint:
In Bohr's atomic model, $\mathrm{T} \propto \mathrm{n}^3$.
Question 33.
The size of atom is proportional to
(a) $\mathrm{A}$
(b) $\mathrm{A}^{1 / 3}$
(c) $\mathrm{A}^{2 / 3}$
(d) $\mathrm{A}^{-1 / 3}$
Answer:
(b) $\mathrm{A}^{1 / 3}$

Question 34.
If an electron jumps from 1st orbit to 3 rd orbit, then it will
(a) not lose energy
(b) not given energy
(c) release energy
(d) absorb energy
Answer:
(d) absorb energy
Hint:
Only by absorbing energy, an electron jumps from first orbit to third orbit.
Question 35.
According to uncertainty principle for an electron, time measurement will become uncertain if following is measured with high certainty
(a) energy
(b) momentum
(c) location
(d) velocity
Answer:
(a) energy
Hint:
According to uncertainty principle, $\Delta \mathrm{E} . \Delta \mathrm{t} \geq \frac{h}{2 \pi}$.
Question 36.
According to Rutherford's atomic model, the electrons inside an atom are
(a) stationary
(b) centralized
(c) non-stationary
(d) none of these
Answer:
(c) non-stationary
Hint:
According to Rutherford model, the electron inside an atom cannot be stationary.
Question 37.
Wavelength of a light emitted from second orbit to first orbit in a hydrogen atom is
(a) $1.215 \times 10^{-7} \mathrm{~m}$
(b) $1.215 \times 10^{-5} \mathrm{~m}$

(c) $1.215 \times 10^{-4} \mathrm{~m}$
(d) $1.215 \times 10^{-3} \mathrm{~m}$
Answer:
(a) $1.215 \times 10^{-7} \mathrm{~m}$
Hint:
$
\begin{aligned}
\frac{1}{\lambda} & =\mathrm{R}\left[\frac{1}{1^2}-\frac{1}{2^2}\right]=\frac{3 \mathrm{R}}{4} \\
\lambda & =\frac{4}{3 \mathrm{R}}=\frac{4}{3 \times 1.097 \times 10^7}=1.215 \times 10^{-7} \mathrm{~m}
\end{aligned}
$
Question 38 .
In terms of Rydberg constant $\mathrm{R}$, the wave number of the first Balmer line is
(a) $R$
(b) $3 R$
(c) $\frac{5 R}{36}$
(d) $\frac{8 R}{9}$
Answer:
(c) $\frac{5 R}{36}$
Hint:
For the first Balmer line, $\bar{v}=\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{2^2}-\frac{1}{3^2}\right)=\frac{5 R}{36}$.
Question 39.
The $\mathrm{K}_\alpha \mathrm{X}$-ray emission line of tungsten occurs at $\lambda=0.021 \mathrm{~nm}$. The energy difference between $\mathrm{K}$ and $\mathrm{L}$ levels in this atom is about
(a) $0.51 \mathrm{MeV}$
(b) $1.2 \mathrm{MeV}$
(c) $59 \mathrm{keV}$
(d) 136
Answer:
(c) $59 \mathrm{keV}$
Hint:
$
\mathrm{E}=\frac{h c}{\lambda}=\frac{6.6 \times 10^{-34} \times 3 \times 10^8}{0.021 \times 10^{-9}} \mathrm{eV}=589.3 \times 10^2 \mathrm{eV} \approx 59 \mathrm{KeV} \text {. }
$

Question 40.
The radius of an electron orbit in a hydrogen atom is of the order of
(a) $10^{-8} \mathrm{~m}$
(b) $10^{-9} \mathrm{~m}$
(c) $10^{-11} \mathrm{~m}$
(d) $10^{-13} \mathrm{~m}$
Answer:
(c) $10^{-11} \mathrm{~m}$
Question 41.
Which of the following atoms has the lowest ionisation potential?
(a) ${ }_7^{14} \mathrm{~N}$
(b) ${ }_{55}^{133} C s$
(c) ${ }_{18}^{40} \mathrm{Ar}$
(d) ${ }_8^{16} \mathrm{O}$
Answer:
(b) ${ }_{55}^{133} C s$
Hint:
In ${ }_{55}^{133} \mathrm{Cs}$, the outermost electron is farthest from the nucleus and so minimum energy is required to remove this electron from the atom. Hence ${ }_{55}^{133} \mathrm{Cs}$ has lowest concision potential.
Question 42.
The transition from the state $\mathrm{n}=4$ to $\mathrm{n}=3$ in a hydrogen like atom result in ultraviolet radiation. Infrared radiation will be obtained in the transition from
(a) $2 \rightarrow 1$
(b) $3 \rightarrow 2$
(c) $4 \rightarrow 2$
(d) $5 \rightarrow 4$
Answer:
(d) $5 \rightarrow 4$
Hint:

The energy gap between $4^{\text {th }}$ and $3^{\text {rd }}$ states is more than the gap between $5^{\text {th }}$ and $4^{\text {th }}$ states.
Question 43.
The number of waves, contained in unit length of the medium, is called
(a) elastic wave
(b) wave number
(c) wave pulse
(d) electromagnetic wave
Answer:
(b) wave number
Hint:
The number of waves contained in a unit length of the medium is called a wave number.
Question 44.
When hydrogen atom is in its first excited level, its radius is
(a) sarhe
(b) half
(c) twice
(d) four times
Answer:
(d) four times
Hint:
$\mathrm{r}_2=\mathrm{r}_1(2)^2=4 \mathrm{r}_1$
Question 45.
The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}$. What is the potential energy of the electron in this state?
(a) $0 \mathrm{eV}$
(b) $-27.2 \mathrm{eV}$
(c) $1 \mathrm{eV}$
(d) $2 \mathrm{eV}$
Answer:
(b) $-27.2 \mathrm{eV}$
Hint:
$P E=2 \times$ Total energy $=2 \times(-13.6)=-27.2 \mathrm{eV}$.

Question 46.
For ionising an excited hydrogen atom, the energy required (in $\mathrm{eV}$ ) will be
(a) a little less than 13.6
(b) 13.6
(c) more than $13.6 \mathrm{eV}$
(d) 3.4 or less
Answer:
(d) 3.4 or less
Hint:
The energy of the electron is $-3.4 \mathrm{eV}$ in first excited state and the its magnitude is less for higher excited state.
Question 47.
What is the energy of $\mathrm{He}^{+}$electron in first order?
(a) $40.8 \mathrm{eV}$
(b) $-27.2 \mathrm{eV}$
(c) $-54.4 \mathrm{eV}$
(d) $-13.6 \mathrm{eV}$
Answer:
(c) $-54.4 \mathrm{eV}$
Hint:
For hydrogen like atoms or ions, $\mathrm{E}_{\mathrm{n}}=\frac{-13.6 Z^2}{n^2} \mathrm{eV}$
For $\mathrm{He}^{+}, \mathrm{Z}=2$ and $\mathrm{n}=1$
$
\mathrm{E}_1=\frac{-13.6 \times 2^2}{12} 54.4 \mathrm{eV}
$

Question 48.
If voltage across on $\mathrm{X}$-ray tube is doubled, then energy of $\mathrm{X}$-ray emitted by
(a) be doubled
(b) be quadrupled
(c) become half
(d) remain the same
Answer:
(d) remain the same
Hint:
The energy of the $\mathrm{X}$-rays depends on the nature of the target material. Thus the energy of the X-rays remain the same.
Question 49.
When hydrogen atom is in its first excited level, its radius is of the Bohr radius.
(a) twice
(b) 4 times
(c) same
(d) half
Answer:
(b) 4 times
Hint:
For first excited level, $\mathrm{n}=2$
$
\mathrm{r}_2=(2)^2 \mathrm{r}_0=4 \mathrm{r}_0
$
Question 50.
The ionisation energy of hydrogen atom is $13.6 \mathrm{eV}$, the ionisation energy of a singly ionsed helium atom would be
(a) $13.6 \mathrm{eV}$
(b) $27.2 \mathrm{eV}$
(c) $6.8 \mathrm{eV}$
(d) $54.4 \mathrm{eV}$
Answer:
(d) $54.4 \mathrm{eV}$
Hint:
$
E_2^1=(2)^2 \mathrm{E}_1=4 \times 13.6=54.4 \mathrm{eV}
$

Question 51.
When an electron makes transition from $n=4$ to $n=2$, then emitted line spectrum will be
(a) first line of lyman series
(b) second line of Balmer series
(c) first line of paschen series
(d) second line of paschen series
Answer:
(b) second line of Balmer series
Hint:
The transition from $\mathrm{n}=4$ to $\mathrm{n}=2$ emits second line of Balmer series.
Question 52.
Maximum frequency of emission is obtained for the transition
(a) $\mathrm{n}=2$ to $\mathrm{n}=1$
(b) $\mathrm{n}=6$ to $\mathrm{n}=2$
(c) $\mathrm{n}=1$ to $\mathrm{n}=2$
(d) $\mathrm{n}=2$ to $\mathrm{n}=6$
Answer:
(a) $\mathrm{n}=2$ to $\mathrm{n}=1$
Hint:
The energy difference $E_2-E_1$ is maximum, so photon of maximum frequency is emitted in transition $\mathrm{n}=2$ to $\mathrm{n}=1$.
Question 53.
Hydrogen atoms are excited from ground state to the state of principle quantum number 4. Then the number of spectral lines observed will be
(a) 3
(b) 6
(c) 5
(d) 2
Answer:
(b) 6
Hint:
Here $\mathrm{n}=4$

$\therefore$ The number of spectral lines emitted $\frac{n(n-1)}{2}=\frac{4 \times 3}{2}=6$
Question 54.
The radius of hydrogen atom, in the ground state is of the order of
(a) $10^{-18} \mathrm{~cm}$
(b) $10^{-7} \mathrm{~cm}$
(c) $10^{-6} \mathrm{~cm}$
(d) $10^{-4} \mathrm{~cm}$
Answer:
(a) $10^{-18} \mathrm{~cm}$
Hint:
Radius of first orbit of $\mathrm{H}$-atom $=0.53 \AA \approx 10^{-8} \mathrm{~cm}$.

Question 56.
According to Bohr's theory of the hydrogen atom, the speed $v_n$ of the electron in a stationary orbit is related to the principal quantum number $\mathrm{n}$ as ( $\mathrm{c}$ is a constant)
(a) $\mathrm{v}_{\mathrm{n}}=\mathrm{c} / \mathrm{n}^2$
(b) $\mathrm{v}_{\mathrm{n}}=\mathrm{c} / \mathrm{n}$
(c) $\mathrm{v}_{\mathrm{n}}=\mathrm{cxn}$
(d) $v_n=c \times n^2$
Answer:
(b) $\mathrm{v}_{\mathrm{n}}=\mathrm{c} / \mathrm{n}$
Hint:
Speed of electron in $\mathrm{n}^{\text {th }}$ orbit, $v_{\mathrm{n}}=\mathrm{c} / \mathrm{n}$.
Question 57.
Out of the following which one is not possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?
(a) $13.6 \mathrm{eV}$
(b) $0.65 \mathrm{eV}$
(c) $1.9 \mathrm{eV}$
(d) $11.1 \mathrm{eV}$
Answer:
(d) $11.1 \mathrm{eV}$
Hint:
For no two energy levels of hydrogen atom, $\mathrm{E}_2-\mathrm{E}_1=11.1 \mathrm{eV}$.
Short Answer Questions
Question 1.
Write down the drawbacks of Rutherford model.
Answer:
1. Drawbacks of Rutherford model:
Rutherford atom model helps in the calculation of the diameter of the nucleus and also the
2. Size of the atom but has the following limitations:
(a) This model fails to explain the distribution of electrons around the nucleus and also the stability of the atom. According to classical electrodynamics, any accelerated charge emits electromagnetic radiations. Due to emission of radiations, it loses its energy.

Hence, it can no longer sustain the circular motion. The radius of the orbit, therefore, becomes smaller and smaller (undergoes spiral motion) and finally the electron should fall into the nucleus and the atoms should disintegrate. But this does not happen. Hence, Rutherford model could not account for the stability of atoms.
(b) According to this model, emission of radiation must be continuous and must give continuous emission spectrum but experimentally we observe only line (discrete) emission spectrum for atoms.
Question 2.
Define excitation potential.
Answer:
Excitation potential is defined as excitation energy per unit charge.
Question 3.
What is meant by atomic number?
Answer:
The number of protons in the nucleus is called the atomic number and it is denoted by $\mathrm{Z}$.
Question 4.
What is meant by neutron number?
Answer:
The number of neutrons in the nucleus is called neutron number $(\mathrm{N})$.
Question 5.
What is meant by mass number?
Answer:
The total number of neutrons and protons in the nucleus is called the mass number and it is denoted by $\mathrm{A}$. Hence, $\mathrm{A}=\mathrm{Z}+\mathrm{N}$.
Question 6.
Write down the properties of neutrino.
Answer:
The neutrino has the following properties:

1. It has zero charge
2. It has an antiparticle called anti-neutrino.
3. Recent experiments showed that the neutrino has very tiny mass.
4. It interacts very weakly with the matter. Therefore, it is very difficult to detect. In fact, in every second, trillions of neutrinos coming from the sun are passing through our body without any interaction.