Characteristics of Bohr's Atomic Model

Q. The total energy of an electron in an atom in an orbit is $-3.4eV$. Its kinetic and potential energies are, respectively

1. $-3.4eV,-3.4eV$
2. $-3.4eV,-6.8eV$
3. $3.4eV,-6.8eV$
4. $3.4eV,3.4eV$

Q. Ionization potential of hydrogen atom is 13.6 V. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. The spectral lines emitted by hydrogen atoms according to Bohr's theory will be

1. three
2. four
3. one
4. two

Q.

The wavelength of the second line in Balmer series of the hydrogen spectrum is 486.4 nm. What is the wavelength of the first line of the Lyman series?

1. None of these
2. 121.6 nm
3. 364.8 nm
4. 729.6 cm

Q.

Obtain the first Bohr’s radius and the ground state energy of a muonic hydrogen atom [i.e., an atom in which a negatively charged muon (μ⁻) of mass about 207m_e orbits around a proton].

Q. The ratio of the energies of the hydrogen atom in its first to second excited state is

1. $\frac{1}{4}$
2. $\frac{4}{9}$
3. $\frac{9}{4}$
4. $4$

Q.

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

Q. The kinetic energy of the electron in an orbit of radius r in hydrogen atom is (e = electronic charge)

1. $\frac{e^2}{r^2}$
2. $\frac{e^2}{2r}$
3. $\frac{e^2}{r}$
4. $\frac{e^2}{2r^2}$

Q. The radius of electron's second stationary orbit in Bohr's atom is R. The radius of the third orbit will be

1. $3R$
2. $2.25R$
3. $9R$
4. $\frac{R}{3}$

Q. An $\alpha$-particle of energy 5 Mev is scattered through ${180}^{\circ }$ by a fixed uranium nucleus the distance of closet approach is of the order of

1. $1\dot{A}$
   
2. ${10}^{-15}cm$
   
3. ${10}^{-12}cm$
   
4. ${10}^{-10}cm$

Q. The ionisation potential of hydrogen atom is 13.6 volt. The energy required to remove an electron in the n = 2 state of the hydrogen atom is

1. 27.2 eV
2. 13.6 eV
3. 6.8 eV
4. 3.4 eV

Q. In an atom, the two electrons move round the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is

1. $\frac{4}{1}$
2. $\frac{8}{1}$
3. $\frac{1}{4}$
4. $\frac{1}{8}$

Q. Energy levels A, B, C of a certain atom corresponding to increasing values of energy i.e. $E_A<E_B<E_C$. If ${\lambda }_1,{\lambda }_2,{\lambda }_3$ are the wavelengths of radiations corresponding to the transitions C to B, B to A and C to A respectively, which of the following statements is correct

1. ${\lambda }_3={\lambda }_1+{\lambda }_2$
2. ${\lambda }_3=\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$
3. ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$
4. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$

Q. Consider an equation represented by,
$b=\frac{ma}{k}\left[\sqrt{1+\frac{2kl}{ma}}\right]$, where, $m$ represents mass, $a$ represents acceleration, $l$ represents length and $k$ is a constant. The SI unit of $b$ should be

1. $\text{s}$
2. $\text{kg}$
3. $\text{m}$
4. $\text{K}$

Q. The energy of hydrogen atom in nth orbit is $E_n$, then the energy in nth orbit of singly ionised helium atom will be

1. $4E_n$
2. $2E_n$
3. $\frac{E_n}{4}$
4. $\frac{E_n}{2}$

Q. If an orbital electron of the hydrogen atom jumps from the ground state to a higher energy state, its orbital speed reduces to half its initial value. If the radius of the electron orbit in the ground state is r, then the radius of the new orbit would be

1. 2r
2. 4r
3. 8r
4. 16r

Q. The wavelength of the first line in Balmer series in the hydrogen spectrum is $\lambda$. What is the wavelength of the second line?

1. $\frac{5}{36}\lambda$
2. $\frac{20}{27}\lambda$
3. $\frac{3}{4}\lambda$
4. $\frac{3}{16}\lambda$

Q. If 13.6 ev energy is required to ionise the hydrogen atom, then the energy required to remove an electron from first exited state (n = 2) is

1. 10.2 eV
2. 0 eV
3. 3.4 eV
4. 6.8 eV

Q.

What is a charge on a one-mole electron known as?

Q. An electron jumps from the $4^{th}$ orbit to the $2^{nd}$ orbit of hydrogen atom. Given the Rydberg's constant $R={10}^{5}c{m}^{-1}$. The frequency in Hz of the emitted radiation will be

1. $\frac{3}{16}\times {10}^5$
2. $\frac{3}{16}\times {10}^{15}$
3. $\frac{9}{16}\times {10}^{15}$
4. $\frac{3}{4}\times {10}^{15}$

Q. Nuclear radius of ${}^{27}Al$ is $3.6\times {10}^{-15}\text{m}$, approximate radius of ${}^{64}Cu$ is

1. $4.8\times {10}^{-15}\text{m}$
2. $2.4\times {10}^{-15}\text{m}$
3. $1.2\times {10}^{-15}\text{m}$
4. $6.4\times {10}^{-15}\text{m}$

Q. As a result of change in magnetic flux linked to the stationary closed loop placed perpendicular to the magnetic field as shown in the figure, an emf of magnitude $V$ is induced in the loop. The work done in moving a charge $Q$, once around the loop is -

1. $QV$
2. $2QV$
3. $\frac{QV}{2}$
4. Zero

Q. The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom is

1. 16 : 1
2. 18 : 1
3. 4 : 1
4. 2 : 1

Q.

What is BM in magnetic moment?

Q. The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by
$E=\frac{3}{5}\frac{Z(Z-1)e^2}{4\pi {\epsilon }_{0}R}$
The measured masses of the neutron, ${}_1^{1}H,{}_7^{15}N$ and ${}_8^{15}O$ are $1.008665u,1.007825u,15.000109u$ and $15.003065u$ respectively. Given that the radii of both the ${}_7^{15}N$ and ${}_8^{15}O$ nuclei are same, $1u=931.5MeV/c^2$ ($c$ is the speed of light) and $e^2/\left(4\pi {\epsilon }_0\right)=1.44MeVfm$. Assuming that the difference between the binding energies of ${}_7^{15}N$ and ${}_8^{15}O$ is purely due to the electrostatic energy, the radius of either of the nuclei is $(1fm={10}^{-15}m)$

1. $2.85fm$
2. $3.03fm$
3. $3.42fm$
4. $3.80fm$

Q. In Bohr’s model of hydrogen atom, the ratio between the period of revolution of an electron in orbit n = 1 to the period of the electron in the orbit n = 2 is

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

Q.

Ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is

1. $5/27$
2. $3/23$
3. $7/29$
4. $9/31$

Q.

Choose the correct option for the below-given statements.
Statement I: In Bohr’s model, the velocity of electrons increases with a decrease in the positive charge of the nucleus as electrons are not held tightly.

Statement II: Velocity decreases with an increase in principal quantum number.

1. Statement I is correct & Statement II is correct

2. Statement I is correct & Statement II is incorrect

3. Statement I is incorrect & Statement II is incorrect

4. Statement I is incorrect & Statement II is correct

Q. In which of the following systems will the radius of the first orbit be minimum

1. Hydrogen atom
2. Deuterium atom
3. Singly ionized helium
4. Doubly ionized lithium

Q. Double ionised helium atom and hydrogen ions are accelerated from rest , through the same potential difference . The ratio of final velocity of helium and hydrogen is
Correct option is 1:2^-1/2

Q. Ionisation energy for hydrogen atom in the ground state is E. What is the ionisation energy of $L{i}^{++}$ atom in the $2^{nd}$ excited state

1. E
2. 3 E
3. 6 E
4. 9 E