Bohr's Postulates

Q. A hydrogen atom in ground state absorbs $10.2\text{eV}$ of energy. The orbital angular momentum of the electron is increased by

1. $1.05\times {10}^{-34}\text{Js}$
2. $2.11\times {10}^{-34}\text{Js}$
3. $3.16\times {10}^{-34}\text{Js}$
4. $4.22\times {10}^{-34}\text{Js}$

Q.

The force acting on the electron in a hydrogen atom depends on the principal quantum number as :

1. $\mathrm{F}\propto {\mathrm{n}}^2$

2. $\mathrm{F}\propto {\mathrm{n}}^4$

3. $\mathrm{F}\propto \frac{1}{{\mathrm{n}}^2}$

4. $\mathrm{F}\propto \frac{1}{{\mathrm{n}}^4}$

Q. Using Bohr's postulates, derive the expression for the frequency of radiation emitted when an electron in a hydrogen atom undergoes transition from a higher energy state (quantum number $n_i$) to a lower state, $\left(n_f\right)$.
When an electron in a hydrogen atom jumps from energy state $n_i=4$ to $n_f=3,2,1,$ identify the spectral series to which the emission lines belong.

Q.

How does Ionization Potential vary in a group and a period?

Q. A photon collides with a stationary hydrogen atom in ground state, inelastically. The energy of the colliding photon is $10.2\text{eV}$. Almost instantaneously, another photon collides with the same hydrogen atom inelastically, with an energy of $15\text{eV}$. What will be observed by the detector?

1. One photon of energy $10.2\text{eV}$ and one electron of energy $1.4\text{eV}$
2. One electron having kinetic energy nearly $11.6\text{eV}$
3. Two photons of energy $1.4\text{eV}$
4. Two photons of energy $10.2\text{eV}$

Q. The ground state energy of hydrogen atom is $-13.6\text{eV}$. When its electron is in the first excited state, its excitation energy is

1. $0$
2. $6.8\text{eV}$
3. $3.4\text{eV}$
4. $10.2\text{eV}$

Q. Two positive ions, each carrying a charge $q$, are separated by a distance $d$. If $F$ is the force of repulsion between the ions, the number of electrons missing from each ion will be ($e$ being the charge on an electron)

1. $\frac{4\pi {ϵ}_{0}F{d}^2}{e^2}$
2. $\sqrt{\frac{4\pi {ϵ}_{0}F{e}^2}{d^2}}$
3. $\sqrt{\frac{4\pi {ϵ}_{0}F{d}^2}{e^2}}$
4. $\frac{4\pi {ϵ}_{0}F{d}^2}{q^2}$

Q.

What is Oxygen Ionization energy?

Q.

What is Copper Fermi Energy?

Q.

What is the angular momentum for $p$-shell electron ?

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

2. Zero

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

4. none

Q.

What is meant by “ discrete nature of charge” ?

Q.

According to Bohr’s postulate, the angular momentum in stationary orbits is:

1. Not quantized

2. Can’t comment

3. Quantized but he did not propose a value

4. Quantized and is equal to $\frac{nh}{2\pi },$ where n is the quantum number of the orbit

Q.

Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.

Q.

Why does F have larger Ionization energy than O?

Q.

A charged particle (electron or proton) is introduced at the origin $(x=0,y=0,x=0)$ with a given initial velocity $\overrightarrow{v}$. A uniform electric field $\overrightarrow{E}$ and a uniform magnetic field $\overrightarrow{B}$ exist everywhere. The velocity $\overrightarrow{v}$, electric field $\overrightarrow{E}$ and magnetic field $\overrightarrow{B}$ are given in column $1,2$ and $3,$ respectively. The quantities $E_0,B_0$ are positive in magnitude.

Column 1	Column 2	Column 3
$\left(I\right)$ Electron with $\overrightarrow{v}=2\frac{E_0}{B_0}\hat{x}$	$\left(i\right)$ $\overrightarrow{E}=E_0\hat{z}$	$\left(P\right)$ $\overrightarrow{B}=-B_0\hat{x}$
$\left(II\right)$ Electron with $\overrightarrow{v}=\frac{E_0}{B_0}\hat{y}$	$\left(ii\right)$ $\overrightarrow{E}=-E_0\hat{y}$	$\left(Q\right)$ $\overrightarrow{B}=-B_0\hat{x}$
$\left(III\right)$ Electron with $\overrightarrow{v}=0$	$\left(iii\right)$ $\overrightarrow{E}=-E_0\hat{x}$	$\left(R\right)$ $\overrightarrow{B}=B_0\hat{y}$
$\left(IV\right)$ Electron with $\overrightarrow{v}=2\frac{E_0}{B_0}\hat{x}$	$\left(iv\right)$ $\overrightarrow{E}=E_0\hat{x}$	$\left(S\right)$ $\overrightarrow{B}=B_0\hat{z}$

In which case will the particle move in a straight line with constant velocity?

1. $\left(IV\right)\left(i\right)\left(S\right)$
2. $\left(II\right)\left(iii\right)\left(S\right)$
3. $\left(III\right)\left(iii\right)\left(P\right)$
4. $\left(III\right)\left(ii\right)\left(R\right)$

Q. The minimum angular momentum of electron of hydrogen atom in stationary orbit is

1. $\frac{h}{2\pi }$
2. $\frac{3h}{2\pi }$
3. $\frac{h}{4\pi }$
4. $\frac{5h}{2\pi }$

Q. An electron in Bohr's hydrogen atom has an energy of $-3.4eV$. The angular momentum of the electron is

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

Q. Which of the following transitions in a hydrogen atom, will emit photon of highest frequency?

1. $n=1\to n=2$
2. $n=2\to n=1$
3. $n=2\to n=6$
4. $n=6\to n=2$

Q. A source of sound is travelling with a velocity of $30\text{m/s}$ towards a stationary observer. If actual frequency of the source is $800\text{Hz}$ and the wind is blowing with velocity $10\text{m/s}$ in a direction making an angle ${60}^{\circ }$ with the direction of motion of the source, then the apparent frequency heard by the observer is:
(speed of sound in still air is $340\text{m/s}$)

1. $800\text{Hz}$
2. $825\text{Hz}$
3. $876\text{Hz}$
4. $1000\text{Hz}$

Q. If Bohr’s quantisation postulate (angular momentum = nh/2π) is abasic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbitsof planets around the sun?

Q.

Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen ?

Q. Write three postulates of Bohr. Mention two limitations of Bohr model.

Q. A source is moving with constant speed $v_s=20\text{m/s}$ towards a stationary observer due east of the source. Wind is blowing at the speed of $20\text{m/s}$ at ${60}^{\circ }$ north of east. The source has frequency $1000\text{Hz}$. If the speed of sound is $310\text{m/s}$, the frequency observed by the observer is approximately

1. $1000\text{Hz}$
2. $1500\text{Hz}$
3. $1067\text{Hz}$
4. $1200\text{Hz}$

Q. Drawbacks of Bohr's atomic model :

Q.

To explain his theory Bohr used:

1. conservation of quantum frequency

2. conservation of linear momentum

3. conservation of angular momentum

4. conservation of energy

Q. What is meant by 'Quantization of charge'?

Q. Ionisation potential of $L{i}^{++}$ in ground state is

1. 13.6 V
2. 122.4 V
3. 54.4 V
4. 3.4 V

Q. Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10–10m). (a) Construct a quantity with the dimensions of length from the fundamental constants e, me , and c. Determine its numerical value. (b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me , and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.

Q. Which of these are Bohr's postulates?

1. In an atom, the electrons revolve around the nucleus in certain definite circular paths called stationary orbits in which they do not radiate energy.
2. Electron revolves around nucleus only in those orbits for which the angular momentum is an integral multiple of
3. Atoms with more than 1 electron will have subshells present in their permissible orbits.
4. An electron present in an atom can move from a lower energy level to a level of higher energy by absorbing the appropriate energy.

Q.

A source of sound $S$ is moving with a velocity of $50m/s$ towards a stationary observer. The observer measures the frequency of the source as $1000Hz$ when source is moving towards observer. What will be the frequency of the source when it is moving away from the observer after crossing him? (Take the velocity of sound in air as $350m/s$)

1. $750Hz$

2. $857Hz$

3. $1143Hz$

4. $807Hz$