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A particular hydrogen - like ion emits the radiation of frequency $3 \times 10^{15} Hz$ when it makes transition from $n = 2$ to $n = 1 .$ The frequency of radiation emitted in transition from $n =3$ to $n = 1$ is $\frac{x}{9} \times 10^{15} Hz,$ when $x =$ _____.

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Important Questions on Structure of Atoms and Nuclei

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

L i^{+ +}

,electron in first Bohr orbit is excited to a level by a radiation of wavelength

λ

.When the ion gets de excited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of

λ

?
(Given:

h = 6.63 \times 10^{- 34} J s; c = 3 \times 10^{8} m s^{- 1}

)

MEDIUM

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

The acceleration of an electron in the first orbit of the hydrogen atom (

n = 1

) is :

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

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius

4.65 Å

). The de-Broglie wavelength of this electron is:

EASY

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

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>Bohr Model

To calculate the size of a hydrogen anion using the Bohr model, we assume that its two electrons move in an orbit such that they are always on diametrically opposite sides of the nucleus. With each electron having the angular momentum,

♄ = \frac{h}{2 π},

and taking electron interaction into account the radius of the orbit in terms of the Bohr radius of a hydrogen atom

a_{B} = \frac{4 π ε_{0} h^{2}}{m e^{2}}

MEDIUM

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

An excited

{H e}^{+}

ion emits two photons in succession, with wavelengths

108.5 n m

and

30.4 n m

in making a transition to the ground state. The quantum number

n

, corresponding to its initial excited state is
(for a photon of wavelength

λ

, energy

E = \frac{1240 eV}{λ (in nm)}

)

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,

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

Consider third orbit of ${He}^{+}$ (helium), using non-relativistic approach, the speed of electron in this orbit will be given constant $K {=9×10}^{9}$ , $Z =2$ and $h$ (Planck's Constant) $= 6 .6 \times 10^{- 34} J s$

EASY

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

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>Bohr Model

In a hydrogen atom the electron makes a transition from

{(n + 1)}^{th}

level to the

n^{th}

level. If

n > > 1

, the frequency of radiation emitted is proportional to :

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:

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}

).........

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

Highly excited states for hydrogen like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >> 1. Which of the following statement(s) is (are) true?

EASY

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

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

EASY

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

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

EASY

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

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>Bohr Model

An electron in a hydrogen atom jumps from second Bohr orbit to ground state and the energy difference of the two states is radiated in the form of photons. These are then allowed to fall on a metal surface having a work-function equal to

4.2 eV

, then the stopping potential is [Energy of electron in

n^{th}

orbit

= - \frac{13 .6}{n^{2}} eV

]

EASY

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

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>Bohr Model

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion

A particular hydrogen - like ion emits the radiation of frequency 3×1015 Hz when it makes transition from n=2 to n=1. The frequency of radiation emitted in transition from n=3 to n=1 is x9×1015 Hz, when x= _____.

Important Questions on Structure of Atoms and Nuclei

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A particular hydrogen - like ion emits the radiation of frequency $3 \times 10^{15} Hz$ when it makes transition from $n = 2$ to $n = 1 .$ The frequency of radiation emitted in transition from $n =3$ to $n = 1$ is $\frac{x}{9} \times 10^{15} Hz,$ when $x =$ _____.