Atomic Structure | Physics JEE previous year questions with Solutions

Q 1 :
According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

$\frac{h}{2 π}$
$8 \frac{h}{π}$
$2 \frac{h}{π}$
$\frac{h}{π}$

1

2

3

4

(C) Moment of momentum or angular momentum, $L = \frac{n h}{2 π}$

put $n = 4$

$L = \frac{4 h}{2 π} = \frac{2 h}{π}$

Q 2 :
An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is [2024]

2E = 3U
E = 2U
E = U
2E = U

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2

3

4

(D) Total energy $E = \frac{- k Z e^{2}}{2 r}$

Potential energy $U = \frac{- k Z e^{2}}{r} \Rightarrow U = 2 E$

Q 3 :
In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

$10^{39}$
$10^{19}$
$10^{29}$
$10^{36}$

1

2

3

4

(A) $F_{e} = \frac{k Q_{1} Q_{2}}{r^{2}} = \frac{9 \times 10^{9} \times 1.6 \times 10^{- 19} \times 1.6 \times 10^{- 19}}{r^{2}}$

$F_{g} = \frac{G m_{1} m_{2}}{r^{2}} = \frac{6.67 \times 10^{- 11} \times 9.1 \times 10^{- 31} \times 1.6 \times 10^{- 27}}{r^{2}}$

$\frac{F_{e}}{F_{g}} ≅ 0.23 \times 10^{40} ≅ 2.3 \times 10^{39}$

Q 4 :
The angular momentum of an electron in a hydrogen atom is proportional to

(Where r is the radius of orbit of electron) [2024]

$\frac{1}{r}$
$r$
$\sqrt{r}$
$\frac{1}{\sqrt{r}}$

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2

3

4

(C) The radius of $n^{t h}$ orbit is, $r \propto \frac{n^{2}}{Z}, \Rightarrow n \propto \sqrt{Z r}$ ...(i)

where, Z is atomic number.

Angular momentum is given by, $L = \frac{n h}{2 π}$ ...(ii)

Put value of $n$ from (i) to equation (ii),

$L = \frac{\sqrt{Z r} h}{2 π} = (\frac{\sqrt{Z} h}{2 π}) \sqrt{r} \Rightarrow L \propto \sqrt{r}$

Q 5 :
A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons? [2024]

6
3
10
1

1

2

3

4

(D) $As, E_{n} \propto \frac{Z^{2}}{n^{2}}$

$Energy of the 2 nd orbit E_{2} = \frac{- 13.6}{4} = - 3.4 eV$

$Δ E_{2 \to 1} = 10.2 eV$

$So, only possible transition is from n = 2 to n = 1$

Q 6 :
The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

$\frac{4}{3} R$
$\frac{16}{9} R$
$\frac{3}{4} R$
$\frac{9}{16} R$

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2

3

4

(B) $r \propto \frac{n^{2}}{Z}$

$\frac{r_{4}}{r_{3}} = \frac{4^{2}}{3^{2}} \Rightarrow r_{4} = \frac{16}{9} R$

Q 7 :
Given below are two statements:

Statement I: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.

Statement II: An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

In the light of the above statements, choose the most appropriate from the given below:

Statement I is true but Statement II is false
Both Statement I and Statement II are true
Both statement I and statement II are false
Statement I is false but Statement II is true

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2

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(A) According to Rutherford atomic model, most of mass of atom and all its positive charge is concentrated in tiny nucleus and electron revolve around it.

According to Thomson atomic model, atom is spherical cloud of positive charge with electron embedded in it.

Hence, Statement I is true but statement II is false.

Q 8 :
The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is: [2024]

4
1/4
1/2
1

1

2

3

4

(C) In Bohr's model, for a given state or orbit

$K E = - \frac{P E}{2}$ or $| K E | = \frac{| P E |}{2}$

therefore, $\frac{| K E |}{| P E |} = \frac{1}{2}$

Q 9 :
An electron revolving in $n^{t h}$ Bohr orbit has magnetic moment $μ_{n} .$ If $μ_{n}$ $α$ $n^{x}$ , the value of $x$ is [2024]

2
1
3
0

1

2

3

4

(B) $Magnetic moment (m) = I A$

$= \frac{e}{T} \cdot π r^{2} = \frac{e}{(\frac{2 π r}{v})} \cdot π r^{2} = \frac{e r v}{2}$

$We know that r \propto n^{2} and v \propto \frac{1}{n}$

$S o μ \propto r v$

$μ \propto \frac{n^{2}}{n} \Rightarrow μ \propto n = 1$

Q 10 :
Radius of a certain orbit of hydrogen atom is 8.48 $Å$ . If energy of electron in this orbit is $E / x$ , then $x$ =

(Given $a_{0}$ = 0.529 $Å$ , E = energy of electron in ground state). [2024]

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(16) $We know, r = r_{0} \cdot \frac{n^{2}}{Z} = 0.529 \frac{n^{2}}{Z}$

$For hydrogen, Z = 1$

$8.48 = 0.529 n^{2}; n^{2} = 16; n = 4$

$Energy of electron in n^{t h} orbit {(E)}^{'} = \frac{E}{n^{2}} = \frac{E}{16} \Rightarrow x = 16$

Topic Question Set

Q 1 :
According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

Q 2 :
An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is [2024]

Q 3 :
In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

Q 4 :
The angular momentum of an electron in a hydrogen atom is proportional to

(Where r is the radius of orbit of electron) [2024]

Q 5 :
A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons? [2024]

Q 6 :
The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

Q 8 :
The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is: [2024]

Q 9 :
An electron revolving in $n^{t h}$ Bohr orbit has magnetic moment $μ_{n} .$ If $μ_{n}$ $α$ $n^{x}$ , the value of $x$ is [2024]

Q 10 :
Radius of a certain orbit of hydrogen atom is 8.48 $Å$ . If energy of electron in this orbit is $E / x$ , then $x$ =

(Given $a_{0}$ = 0.529 $Å$ , E = energy of electron in ground state). [2024]

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Topic Question Set

Q 1 : According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

Q 2 : An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is [2024]

Q 3 : In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

Q 4 : The angular momentum of an electron in a hydrogen atom is proportional to (Where r is the radius of orbit of electron) [2024]

Q 5 : A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons? [2024]

Q 6 : The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

Q 8 : The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is: [2024]

Q 9 : An electron revolving in nth Bohr orbit has magnetic moment μn. If μn α nx, the value of x is [2024]

Q 10 : Radius of a certain orbit of hydrogen atom is 8.48 Å. If energy of electron in this orbit is E/x, then x= (Given a0 = 0.529 Å, E = energy of electron in ground state). [2024]

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Q 1 :
According to Bohr's theory, the moment of momentum of an electron revolving in 4th orbit of hydrogen atom is [2024]

Q 2 :
An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is [2024]

Q 3 :
In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

Q 4 :
The angular momentum of an electron in a hydrogen atom is proportional to

(Where r is the radius of orbit of electron) [2024]

Q 5 :
A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons? [2024]

Q 6 :
The radius of third stationary orbit of electron for Bohr's atom is P. The radius of fourth stationary orbit will be [2024]

Q 8 :
The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5th excited state of a hydrogen atom is: [2024]

Q 9 :
An electron revolving in $n^{t h}$ Bohr orbit has magnetic moment $μ_{n} .$ If $μ_{n}$ $α$ $n^{x}$ , the value of $x$ is [2024]

Q 10 :
Radius of a certain orbit of hydrogen atom is 8.48 $Å$ . If energy of electron in this orbit is $E / x$ , then $x$ =

(Given $a_{0}$ = 0.529 $Å$ , E = energy of electron in ground state). [2024]