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The de-Broglie wavelength associated with electrons revolving round the nucleus in a singly ionised helium atom in first excited state, will be

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Important Questions on Structure of Atoms and Nuclei

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

A hydrogen atom in ground state absorbs

10.2 e V

of energy. The orbital angular momentum of the electron is increased by

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

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

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

According to Bohr's theory of the hydrogen atom, the radii

r_{n}

of stationary electron orbits are related to the principal quantum number

n

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths

λ_{N}, λ_{A}

respectively. The ratio

\frac{λ_{N}}{λ_{A}}

is closest to:

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

12 eV

energy is given to electron in third orbit of

H

-atom, then final energy of electron when it ionise from third orbit, is

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

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

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

A hydrogen atom is in a state with energy

- 1.51 eV

. In the Bohr model, the angular momentum of the electron in the atom with respect to an axis at the nucleus, is

(\frac{h}{2 π} = 1.05 \times 10^{- 34} J s)

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

An electron with kinetic energy

E

collides with a hydrogen atom in the ground state. The collision will be elastic

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

Radiation coming from transitions

n = 2

n = 1

of hydrogen atoms fall on

{H e}^{+}

ions in

n = 1

and

n = 2

states. The possible transition of helium ions as they absorb energy from the radiation is:

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

In the hydrogen atom spectrum, let

E_{1}

and

E_{2}

are energies for the transition

n = 2 \to n = 1

and

n = 3 \to n = 2

respectively. The ratio

E_{2} / E_{1}

EASY

Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

A particle of mass,

m

moves around the origin in a potential,

\frac{1}{2} m ω^{2} r^{2}

, where

r

is the distance from the origin. Applying the Bohr model in this case, the radius of the particle in its

n^{th}

orbit in terms of

a = \sqrt{\frac{h}{(2 π m ω)}}

is,

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

Angular momentum of an electron in hydrogen atom is

\frac{3 h}{2 π}

(

h

is the Planck's constant). The K.E. of the electron is

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

A particle

A

of mass

m

and charge

q

is accelerated by a potential difference of

50 V .

Another particle

B

of mass

4 m

and charge

q

is accelerated by a potential difference of

2500 V .

The ratio of de-Broglie wavelengths

\frac{λ_{A}}{λ_{B}}

is close to:

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

Electron in Hydrogen atom first jumps from third excited state to second excited state and then from second excited state to first excited state. The ratio of the wavelengths

λ_{1} : λ_{2}

emitted in the two cases respectively is

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

How the linear velocity $v$ of an electron in the Bohr orbit is related to its quantum number $n ?$

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

The difference between the radii of

n^{th}

and

(n + 1)^{t h}

orbits of hydrogen atom is equal to the radius of

(n - 1)^{th}

orbit of hydrogen. The angular momentum of the electron in the

n^{th}

orbit is

______

(

h

is Planck's constant)

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

The time period of revolution of electron in its ground state orbit in a hydrogen atom is

1.6 \times 10^{- 16} s .

The frequency of revolution of the electron in its first excited state (in

s^{- 1}

) is:

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

The magnitude of acceleration of the electron in the $n^{th}$ orbit of hydrogen atom is $a_{H}$ and that of singly ionised helium atom is $a_{He}$ . The ratio $a_{H} : a_{He}$ is,

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Physics>Modern Physics>Structure of Atoms and Nuclei>de Broglie's Hypothesis

The de-Broglie wavelength of the electron in the first Bohr orbit of the Hydrogen atom is equal to (

a_{B}

denotes the Bohr radius)

The de-Broglie wavelength associated with electrons revolving round the nucleus in a singly ionised helium atom in first excited state, will be

Important Questions on Structure of Atoms and Nuclei

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