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The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

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Important Questions on Atoms

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Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

In a hydrogen like atom electron makes transition from an energy level with quantum number

n

to another with quantum number

(n - 1)

. If

n >> 1

, the frequency of radiation emitted is proportional to :

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

In a Frank - Hertz experiment, an electron of energy

5 .6 eV

passes through mercury vapour and emerges with an energy

0 .7 eV .

The minimum wavelength of photons emitted by mercury atoms is close to:

HARD

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

A free hydrogen atom after absorbing a photon of wavelength

λ_{a}

gets excited from the state

n = 1

to the state

n = 4 .

Immediately after that the electron jumps to

n = m

state by emitting a photon of wavelength

λ_{e} .

Let the change in momentum of atom due to the absorption and the emission are

Δ p_{a}

and

Δ p_{e},

respectively. If

\frac{λ_{a}}{λ_{e}} = \frac{1}{5},

which of the option(s) is/are correct?
[Use

h c = 1242 e V n m, 1 n m = 10^{- 9} m,

h

and

c

are Planck's constant and speed of light, respectively]

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

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}

)

EASY

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

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>Atoms>Bohr Model of the Hydrogen Atom

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:

HARD

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

An electron in a hydrogen atom makes a transition from

n = 2

n = 1

and emits a photon. This photon strikes a doubly ionized lithium atom which was already in an excited state and completely removes the orbiting electron. The least quantum number for the excited state of the lithium-ion for the process is

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

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>Atoms>Bohr Model of the Hydrogen Atom

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

]

HARD

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

The radius of the orbit of an electron in a Hydrogen-like atom is

4.5

a_{0}

, where

a_{0}

is the Bohr radius. Its orbital angular momentum is

\frac{3 h}{2 π} .

It is given that

h

is Planck's constant and

R

is Rydberg constant. The possible wavelengths, when the atom de-excites, is (are)

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

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>Atoms>Bohr Model of the Hydrogen Atom

If an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength

λ

. When it jumps from the fourth orbit to the third orbit, the corresponding wavelength of the photon will be

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

Hydrogen atom in ground state is excited by a monochromatic radiation of

λ = 975 Å .

Number of spectral lines in the resulting spectrum emitted will be:

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths

\frac{λ_{1}}{λ_{2}}

of the photons emitted in this process is:

HARD

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

A difference of

2.3 eV

separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

The total energy of an electron in the

n^{th}

stationary orbit of the hydrogen atom can be obtained by

HARD

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

A particle of mass

m

moves in circular orbits with potential energy

U (r) = F r

, where

F

is a positive constant and

r

is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by

R

and its speed and energy are denoted by

v

and

E

respectively, then for the

n^{th}

orbit (here

h

is the Planck's constant)

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

The wavelength of the first Balmer line caused by a transition from the

n = 3

level to the

n = 2

level in hydrogen is

λ_{1} .

The wavelength of the line caused by an electronic transition from

n = 5

n = 3

EASY

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

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:

MEDIUM

Physics>Modern Physics>Atoms>Bohr Model of the Hydrogen Atom

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

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

Important Questions on Atoms

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