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PHXII12:ATOMS

356408 In Bohr's model of $H$ -atom, the kinetic energy of the electron in any orbit depends on the principal quantum number $n$ as

1

K \propto \frac{1}{n^{2}}

2

K \propto n^{2}

3

K \propto 1 / n^{4}

4

K

does not depend on

n

Explanation:

$K . E . = \frac{1}{2} m v^{2}$ and $v \propto \frac{1}{n}$
$\Rightarrow K . E \propto \frac{1}{n^{2}}$

PHXII12:ATOMS

356409 In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If $a_{0}$ is the radius of the ground state orbit, $m$ is the mass, $e$ is the charge on electron and $ε_{0}$ is the permittivity of free space, the speed of the electron is

1

\frac{e}{\sqrt{ε_{0} a_{0} m}}

2 Zero

3

\frac{e}{\sqrt{4 π ε_{0} a_{0} m}}

4

\frac{\sqrt{4 ε_{0} a_{0} m}}{e}

Explanation:

We can write the expression for the circular motion of electron around the nucleus
$F_{e l e c t r o s t a t i c} = F_{c e n t r i p e t a l}$
$\Rightarrow \frac{1}{4 π ε_{0}} \frac{e^{2}}{a_{0}^{2}} = \frac{m v^{2}}{a_{0}}$
$\Rightarrow v^{2} = \frac{1}{4 π ε_{0}} \frac{e^{2}}{m a_{0}}$
$\Rightarrow v = \frac{e}{\sqrt{4 π ε_{0} a_{0} m}}$

AIIMS - 2009

PHXII12:ATOMS

356410 Assertion :
In hydrogen atom as $n$ increases, energy level comes closer and closer.
Reason :
Energy of an electron in hydrogen atom is $E_{n} = \frac{- 13.6}{n^{2}} e V$

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$E_{n} = - \frac{13.6}{n^{2}} e v$
As $n$ increases energy of the orbits come close to each other. So option (1) is correct.

PHXII12:ATOMS

356411 An electron rotates in a circle around a nucleus having positive charge $Z e$ . Correct relation between total energy $(E)$ of the electron to its potential energy $(U)$ is

1

2 E = 3 U

2

E = 2 U

3

E = U

4

2 E = U

Explanation:

$P E : T E = - 2 : - 1$
$\Rightarrow \frac{P E}{T E} = \frac{2}{1}$
$\Rightarrow \frac{U}{E} = \frac{2}{1}$
$\Rightarrow U = 2 E$

JEE - 2024

PHXII12:ATOMS

356408 In Bohr's model of $H$ -atom, the kinetic energy of the electron in any orbit depends on the principal quantum number $n$ as

1

K \propto \frac{1}{n^{2}}

2

K \propto n^{2}

3

K \propto 1 / n^{4}

4

K

does not depend on

n

Explanation:

$K . E . = \frac{1}{2} m v^{2}$ and $v \propto \frac{1}{n}$
$\Rightarrow K . E \propto \frac{1}{n^{2}}$

PHXII12:ATOMS

356409 In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If $a_{0}$ is the radius of the ground state orbit, $m$ is the mass, $e$ is the charge on electron and $ε_{0}$ is the permittivity of free space, the speed of the electron is

1

\frac{e}{\sqrt{ε_{0} a_{0} m}}

2 Zero

3

\frac{e}{\sqrt{4 π ε_{0} a_{0} m}}

4

\frac{\sqrt{4 ε_{0} a_{0} m}}{e}

Explanation:

We can write the expression for the circular motion of electron around the nucleus
$F_{e l e c t r o s t a t i c} = F_{c e n t r i p e t a l}$
$\Rightarrow \frac{1}{4 π ε_{0}} \frac{e^{2}}{a_{0}^{2}} = \frac{m v^{2}}{a_{0}}$
$\Rightarrow v^{2} = \frac{1}{4 π ε_{0}} \frac{e^{2}}{m a_{0}}$
$\Rightarrow v = \frac{e}{\sqrt{4 π ε_{0} a_{0} m}}$

AIIMS - 2009

PHXII12:ATOMS

356410 Assertion :
In hydrogen atom as $n$ increases, energy level comes closer and closer.
Reason :
Energy of an electron in hydrogen atom is $E_{n} = \frac{- 13.6}{n^{2}} e V$

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$E_{n} = - \frac{13.6}{n^{2}} e v$
As $n$ increases energy of the orbits come close to each other. So option (1) is correct.

PHXII12:ATOMS

356411 An electron rotates in a circle around a nucleus having positive charge $Z e$ . Correct relation between total energy $(E)$ of the electron to its potential energy $(U)$ is

1

2 E = 3 U

2

E = 2 U

3

E = U

4

2 E = U

Explanation:

$P E : T E = - 2 : - 1$
$\Rightarrow \frac{P E}{T E} = \frac{2}{1}$
$\Rightarrow \frac{U}{E} = \frac{2}{1}$
$\Rightarrow U = 2 E$

JEE - 2024

PHXII12:ATOMS

356408 In Bohr's model of $H$ -atom, the kinetic energy of the electron in any orbit depends on the principal quantum number $n$ as

1

K \propto \frac{1}{n^{2}}

2

K \propto n^{2}

3

K \propto 1 / n^{4}

4

K

does not depend on

n

Explanation:

$K . E . = \frac{1}{2} m v^{2}$ and $v \propto \frac{1}{n}$
$\Rightarrow K . E \propto \frac{1}{n^{2}}$

PHXII12:ATOMS

356409 In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If $a_{0}$ is the radius of the ground state orbit, $m$ is the mass, $e$ is the charge on electron and $ε_{0}$ is the permittivity of free space, the speed of the electron is

1

\frac{e}{\sqrt{ε_{0} a_{0} m}}

2 Zero

3

\frac{e}{\sqrt{4 π ε_{0} a_{0} m}}

4

\frac{\sqrt{4 ε_{0} a_{0} m}}{e}

Explanation:

We can write the expression for the circular motion of electron around the nucleus
$F_{e l e c t r o s t a t i c} = F_{c e n t r i p e t a l}$
$\Rightarrow \frac{1}{4 π ε_{0}} \frac{e^{2}}{a_{0}^{2}} = \frac{m v^{2}}{a_{0}}$
$\Rightarrow v^{2} = \frac{1}{4 π ε_{0}} \frac{e^{2}}{m a_{0}}$
$\Rightarrow v = \frac{e}{\sqrt{4 π ε_{0} a_{0} m}}$

AIIMS - 2009

PHXII12:ATOMS

356410 Assertion :
In hydrogen atom as $n$ increases, energy level comes closer and closer.
Reason :
Energy of an electron in hydrogen atom is $E_{n} = \frac{- 13.6}{n^{2}} e V$

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$E_{n} = - \frac{13.6}{n^{2}} e v$
As $n$ increases energy of the orbits come close to each other. So option (1) is correct.

PHXII12:ATOMS

356411 An electron rotates in a circle around a nucleus having positive charge $Z e$ . Correct relation between total energy $(E)$ of the electron to its potential energy $(U)$ is

1

2 E = 3 U

2

E = 2 U

3

E = U

4

2 E = U

Explanation:

$P E : T E = - 2 : - 1$
$\Rightarrow \frac{P E}{T E} = \frac{2}{1}$
$\Rightarrow \frac{U}{E} = \frac{2}{1}$
$\Rightarrow U = 2 E$

JEE - 2024

PHXII12:ATOMS

356408 In Bohr's model of $H$ -atom, the kinetic energy of the electron in any orbit depends on the principal quantum number $n$ as

1

K \propto \frac{1}{n^{2}}

2

K \propto n^{2}

3

K \propto 1 / n^{4}

4

K

does not depend on

n

Explanation:

$K . E . = \frac{1}{2} m v^{2}$ and $v \propto \frac{1}{n}$
$\Rightarrow K . E \propto \frac{1}{n^{2}}$

PHXII12:ATOMS

356409 In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If $a_{0}$ is the radius of the ground state orbit, $m$ is the mass, $e$ is the charge on electron and $ε_{0}$ is the permittivity of free space, the speed of the electron is

1

\frac{e}{\sqrt{ε_{0} a_{0} m}}

2 Zero

3

\frac{e}{\sqrt{4 π ε_{0} a_{0} m}}

4

\frac{\sqrt{4 ε_{0} a_{0} m}}{e}

Explanation:

We can write the expression for the circular motion of electron around the nucleus
$F_{e l e c t r o s t a t i c} = F_{c e n t r i p e t a l}$
$\Rightarrow \frac{1}{4 π ε_{0}} \frac{e^{2}}{a_{0}^{2}} = \frac{m v^{2}}{a_{0}}$
$\Rightarrow v^{2} = \frac{1}{4 π ε_{0}} \frac{e^{2}}{m a_{0}}$
$\Rightarrow v = \frac{e}{\sqrt{4 π ε_{0} a_{0} m}}$

AIIMS - 2009

PHXII12:ATOMS

356410 Assertion :
In hydrogen atom as $n$ increases, energy level comes closer and closer.
Reason :
Energy of an electron in hydrogen atom is $E_{n} = \frac{- 13.6}{n^{2}} e V$

1 Both assertion and reason are correct and reason is the correct explanation of assertion.

2 Both assertion and reason are correct but reason is not the correct explanation of assertion.

3 Assertion is correct but reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$E_{n} = - \frac{13.6}{n^{2}} e v$
As $n$ increases energy of the orbits come close to each other. So option (1) is correct.

PHXII12:ATOMS

356411 An electron rotates in a circle around a nucleus having positive charge $Z e$ . Correct relation between total energy $(E)$ of the electron to its potential energy $(U)$ is

1

2 E = 3 U

2

E = 2 U

3

E = U

4

2 E = U

Explanation:

$P E : T E = - 2 : - 1$
$\Rightarrow \frac{P E}{T E} = \frac{2}{1}$
$\Rightarrow \frac{U}{E} = \frac{2}{1}$
$\Rightarrow U = 2 E$

JEE - 2024

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