Bohr's Model of a Hydrogen Atom

Q.

What is the angular momentum of an electron in d orbital?

Q. Ionization energy of $H{e}^{+}$ is 54.4 eV. The ionization energy of $L{i}^{2+}$ is:

1. 54.4 eV
2. 122.4 eV
3. 27.2 eV
4. 40.8 eV

Q.

For emission line of atomic hydrogen from ni=8 to nf- the plot of wavenumber (v) against (1/n2) will be:(The Rydberg constant, RH is in wave number unit).

1. Non-linear

2. Linear with slope ${\mathrm{R}}_{\mathrm{H}}$

3. Linear with slope – ${\mathrm{R}}_{\mathrm{H}}$

4. Linear with intercept- ${\mathrm{R}}_{\mathrm{H}}$

Q. An electron jumps from a lower orbit to a higher orbit when:

1. Energy is released
2. Energy is absorbed
3. No change in energy
4. It radiates energy

Q. Calculate the ratio of energies of $H{e}^{+}$ for $1^{st}$ & $2^{nd}$ excited state.

1. $9:4$
2. $4:9$
3. $1:4$
4. $4:1$

Q. The velocity of an electron in a certain Bohr's orbit of H-atom bears the ratio 1:550 to the velocity of light. The quantum number n of the orbit is:

1. n = 2
2. n = 5
3. n = 3
4. n = 4

Q. Ratio of radii of second and first orbits of $H$ atom is:

1. $2:1$
2. $4:1$
3. $3:1$
4. $5:1$

Q. The frequency of light emitted for the transition $n=4$ to $n=2$ of $H{e}^{+}$ is equal to the transition in $H$-atom corresponding to which of the following:

1. $n=3$ to $n=1$
2. $n=2$ to $n=1$
3. $n=3$ to $n=2$
4. $n=4$ to $n=3$

Q.

Which of the following is true for Bohr's model?

1. An electron can move only in those orbits for which its angular momentum is an integral multiple of $\frac{h}{2\pi }$

2. Electrons revolve around nucleus in discrete and quantized energy levels/orbits.
3. The energy of an electron in the orbit do not change with time.
4. Electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed.

Q. Find the wavelength of the first line of spectral series of $H{e}^{+}$ ion whose interval between extreme lines is $\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}=27419.25{\text{cm}}^{-1}$
(Take Rydberg's constant $R=109677{\text{cm}}^{-1},\frac{1}{109677}=9.11\times {10}^{-6}cm$)

1. $4685\stackrel{\circ }{A}$
2. $46.85\stackrel{\circ }{A}$
3. $7896\stackrel{\circ }{A}$
4. $78.96\stackrel{\circ }{A}$

Q. Calculate the frequency of the limiting line of Brackett series in the hydrogen spectrum.

1. $2.06\times {10}^{14}{s}^{-1}$
2. $6.02\times {10}^{10}{s}^{-1}$
3. $4.52\times {10}^{16}{s}^{-1}$
4. $2.06\times {10}^{12}{s}^{-1}$

Q. The Bohr model of the atom can explain:

1. The spectrum of hydrogen atom only
2. Spectrum of an atom or ion containing one electron only
3. The spectrum of hydrogen molecule
4. The solar spectrum

Q. If the energy difference between two electronic states is $47.5kcalmo{l}^{-1}$ and the frequency of the light emitted when the electrons drop from a higher state to lower states is $x\times {10}^{14}$, what is the value of $x$?
$(N.h=9.5\times {10}^{-14}kcal{s}^{-1}mo{l}^{-1},\text{where, N is the Avogadro's number and h is the Planck's constant})$

Q. The species which has $5^{th}$ ionisation potential equal to 340 eV is:

1. $B^{+}$
2. $C^{+}$
3. $B$
4. $C$

Q. If in the Bohr's model for unielectronic atom, the time period of revolution is represented as $T_{n,z}$, where, n represents the shell number and $Z$ represents the atomic number then, the value of $T_{1,2}:T_{2,1}$ will be:

1. 8 : 1
2. 1 : 8
3. 1 : 1
4. 1 : 32

Q. In a hydrogen atom, an electronic transition takes place from an initial state (1) to a final state (2). The difference in the orbit radius $(r_1-r_2)$ is 24 times the first Bohr radius. Identify the transition.

1. $5\to 1$
2. $25\to 1$
3. $8\to 3$
4. $7\to 5$

Q. A and B are two elements which form compounds AB₂ and A₂B₃. If 55 gm of AB₂ and 90 gm of A₂B₃ have equal number of moles, then the ratio of atomic mass of A to that of B is

A तथा B दो तत्व हैं जो यौगिक AB₂ तथा A₂B₃ बनाते हैं। यदि 55 gm AB₂ तथा 90 gm A₂B₃ के मोलों की संख्या समान है, तो A तथा B के परमाणु द्रव्यमान का अनुपात है

1. 0.25
2. 4
3. 0.75
4. 3.75

Q. The time period for revolution of electron in a Hydrogen atom state $n_1$ is $T_1$ and time period for revolution of electron in higher orbit $n_2$ is $T_2$. If $\frac{T_2}{T_1}=27$. Which values of $n_1$ and $n_2$ are not possible?

1. $n_1=2,n_2=6$
2. $n_1=3,n_2=6$
3. $n_1=3,n_2=9$
4. $n_1=4,n_2=12$

Q. Which of the following relation is untrue based on Bohr's model of the atom?

1. Velocity of electron $\propto \frac{1}{n}$
2. Frequency of revolution $\propto \frac{1}{n^3}$
3. Radius of orbit $\propto n^{2}Z$
4. Energy of an electron in $n^{th}$orbit $\propto Z^2$

Q.

Identify the angular momentum which is not possible for an electron in Bohrs orbit of a hydrogen atom.

1. $\frac{\mathrm{h}}{\mathrm{\pi }}$

2. $\frac{3\mathrm{h}}{2\mathrm{\pi }}$

3. $\frac{4\mathrm{h}}{\mathrm{\pi }}$

4. $\frac{3\mathrm{h}}{4\mathrm{\pi }}$

Q. The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$a_o$ is radius of first Bohr orbit]:

1. $\frac{h^2}{4{\pi }^{2}m{a_o}^2}$
2. $\frac{h^2}{16{\pi }^{2}m{a_o}^2}$
3. $\frac{h^2}{32{\pi }^{2}m{a_o}^2}$
4. $\frac{h^2}{64{\pi }^{2}m{a_o}^2}$

Q. Which of the following series of transitions in the spectrum of hydrogen atom fall in the visible region?

1. Lyman series
2. Balmer series
3. Paschen series
4. Brackett series

Q. The ratio of the radii of the $2^{nd}$ Bohr orbit of hydrogen atom to $3^{rd}$ Bohr orbits of $L{i}^{2+}$ is:

1. $3:2$
2. $2:3$
3. $3:4$
4. $4:3$

Q. Find the number of waves made by a Bohr electron in one complete revolution in the $3^{rd}$ orbit.

Q. If the ionisation energy of hydrogen atom is $13.6eV$, what will be the ionisation energy of $H{e}^{+}$ and $L{i}^{2+}$ ions respectively?

1. $27.2eV,40.8eV$
2. $13.6eV,54.4eV$
3. $54.4eV,54.4eV$
4. $54.4eV,122.4eV$

Q. How many times does the electron go around the first orbit of hydrogen atom in one second?

1. $13.18\times {10}^{15}$
2. $6.59\times {10}^{13}$
3. $2.07\times {10}^{13}$
4. $6.59\times {10}^{15}$

Q. For emission line of atomic hydrogen from ${\text{n}}_i=8to{n}_f=n$, the plot of wave number ($\stackrel{-}{v}$) against $\frac{1}{n^2}$will be (The Rydberg constant $R_H$ is in wave number unit)

1. Linear with slope -$R_H$
2. Linear with intercept -$R_H$
3. Non-linear
4. Linear with slope $R_H$

Q. The radius of which of the following orbits is the same as that of the first Bohr's orbit of hydrogen atom?

1. $H{e}^{+}(n=2)$
2. $L{i}^{2+}(n=2)$
3. $L{i}^{2+}(n=3)$
4. $B{e}^{3+}(n=2)$

Q. What is the electron separation energy (in $eV$) for $B{e}^{3+}$ in the first excited state.

1. $13.6eV$
2. $27.2eV$
3. $40.8eV$
4. $54.4eV$

Q. If the energy of the electron in hydrogen atom in a certain excited state is $-3.4eV$, then what will be its angular momentum?

1. $\frac{h}{2\pi }$
2. $\frac{h}{\pi }$
3. $\frac{3h}{2\pi }$
4. $\frac{2h}{\pi }$