Show that the total energy of an electron in an atom is negative and is, E = - e 2 8 πε 0 . What is the significance of negative energy?

The total energy of a revolving electron is the sum of its kinetic energy and potential energy. The force between the electron and the proton is given by the Coulomb's law i.e F e = q 1 q 2 4 πε 0 r 2 = e 2 4 πε 0 r 2 ...............................(1) The centripetal force of the revolving electron is given by. F c = mv 2 r ....................................(2) In equilibrium, these forces balance each other i.e mv 2 r = e 2 4 πε 0 r 2 or mv 2 = e 2 4 πε 0 r .....................................(3) The potential energy of electron - proton system is given by, PE = q q 4 πε 0 r = - e 2 4 πε 0 r .....................................(4) From equation (3), the KE of the electron is KE = 1 2 mv 2 = e 2 8 πε 0 r . Therefore, the total energy of the revolving electron is , E = KE + PE = e 2 8 πε 0 r + - e 2 4 πε 0 r = - e 2 8 πε 0 r . A negative value for the energy implies that energy must be supplied to the system if the electron is to overcome the attractive force of the nucleus a nd escape from the atom. Hence ,the electron is bound to the nucleus.

EASY

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If the plank’s constant would be double the present value, in the Bohr’s model for hydrogen atom

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Important Questions on Structure of Atoms and Nuclei

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

A particle of mass

m

moves in a circular orbit in a central potential field

U (r) = \frac{1}{2} k r^{2} .

If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number

n

as:

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The period of revolution of an electron in the ground state of the hydrogen atom is $T$ . The period of revolution of the electron in the first excited state is

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The energy of the electron in an excited state of a hydrogen atom is

- 3.4 eV

. (Given

R_{H} = 1.1 \times 10^{7} m^{- 1}

). Then the angular momentum of the electron is

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Show that the total energy of an electron in an atom is negative and is,

$E = - \frac{e^{2}}{8 {πε}_{0}}$ .

What is the significance of negative energy?

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The total energy of an electron in the first excited state of hydrogen is about

- 3.4 eV

. Its kinetic energy in this state is

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

State the postulates of Bohr atom model. Obtain the expression for the radius of the $n^{th}$ orbit of an electron based of Bohr's theory.

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The total energy of an electron in the first excited state of

H

-atom is

- 3.4 eV

, then its potential energy is in this state is _____

eV

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Write the value of Bohr’s radius.

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

We consider the Thomson model of the hydrogen atom in which the proton charge is distributed uniformly over a spherical volume of radius

0.25 \overset{o}{A}

. Applying the Bohr condition in this model, the ground state energy (in

eV

) of the electron will be close to

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

A photon falls through a height of

1 km

through the earth's gravitational field. To calculate the change in its frequency, take its mass to be

\frac{h v}{c^{2}}

. The fractional change in frequency

v

is close to

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Derive the expression for the total energy of an electron in the

n^{t h}

orbit of hydrogen atom.

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Frequency of revolution of an electron revolving in n^th orbit of H-atom is proportional to

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

If the radius of the first orbit of hydrogen atom is

5.3 \times 10^{- 11} m

, then the radius of the second orbit is.

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The energy of electron in the excited state of hydrogen atom is $- 0.85 eV$ . If $' h'$ is Planck's constant, the angular momentum of electron in the excited state is:

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

If the radius of the first Bohr's orbit is

r

, the radius of second Bohr's orbit is.

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Niels Bohr made certain modification in Rutherford's model by adding the ideas of quantum hypothesis.

Derive an expression for the radius and energy of the electron in the $n^{th}$ orbit of hydrogen atom.

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

Derive an expression for the total energy of an electron in any orbit of a hydrogen atom in accordance with Bohr’s atomic model.

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The relation between force acting on the electron and principle quantum number in Hydrogen atom is

HARD

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

A particle of mass

200 MeV c^{- 2}

collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in

eV

) is

\frac{N}{4} .

The value of

N

is: (Given the mass of the hydrogen atom to be

1 GeV c^{- 2}

).........

MEDIUM

Physics>Modern Physics>Structure of Atoms and Nuclei>Bohr Model

The total energy of an electron in an atom in an orbit is

- 3.4 e V .

Its kinetic and potential energies are, respectively,

If the plank’s constant would be double the present value, in the Bohr’s model for hydrogen atom

Important Questions on Structure of Atoms and Nuclei

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