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The de-Broglie wavelength $L$ associated with an elementary particle of linear momentum $p$ is best represented by the graph

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Important Questions on Dual Nature of Radiation and Matter

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Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de brogile wavelengths are

λ_{1}

and

λ_{2}

, their de brogile wavelength in the frame of reference attached to their centre of mass is:

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Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

A particle

A

of mass

m

and initial velocity

v

collides with a particle

B

of mass

\frac{m}{2}

which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths

λ_{A}

λ_{B}

after the collision is:

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

The mean momentum of a nucleon inside a nucleus with mass number

A

varies as

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

Two particles

A

and

B

of same mass have their de-Broglie wavelengths in the ratio

X_{A} : X_{B} = K : 1 .

Their potential energies

U_{A} : U_{B} = 1 : K^{2} .

The ratio of their total energies

E_{A} : E_{B}

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

De-Broglie wavelength of an electron accelerated by a voltage of

50 V

is close to

(|e| = 1.6 \times 10^{- 19} C, m_{e} = 9.1 \times 10^{- 31} k g, h = 6.6 \times 10^{- 34} J s)

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

Two electrons in two hydrogen-like atoms

A

and

B

have their total energies

E_{A}

and

E_{B}

in the ratio

E_{A} : E_{B} = 1 : 2

. Their potential energies

U_{A}

and

U_{B}

are in the ratio

U_{A} : U_{B} = 1 : 2

. If

λ_{A}

and

λ_{B}

are their de-Broglie wavelengths, then

λ_{A} : λ_{B}

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

According to de-Broglie hypothesis, the wavelength associated with moving electron of mass m is

λ_{e}

. Using mass energy relation and Planck's quantum theory, the wavelength associated with photon is

λ_{p} .

If the energy

(E)

of electron and photon is same then relation between

λ_{e}

and

λ_{p}

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

A nucleus

A,

with a finite de-broglie wavelength

λ_{A},

undergoes spontaneous fission into two nuclei

B

and

C

of equal mass.

B

flies in the same direction as that of

A,

while

C

flies in the opposite direction with a velocity equal to half of that of

B .

The de-Broglie wavelengths

λ_{B}

and

λ_{C}

of B and C are respectively:

HARD

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

An electron in an electron microscope with initial velocity

v_{0} \hat{i}

enters a region of a stray transverse electric field

E_{0} \hat{j}

. The time taken for the change in its de-Broglie wavelength from the initial value of

λ

\frac{λ}{3}

is proportional to,

HARD

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

The de-Broglie wavelength

(λ_{B})

associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state

(λ_{G})

by:

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

The de-Broglie wavelength

λ_{n}

of the electron in the

n^{t h}

orbit of hydrogen atom is

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

The kinetic energy of an electron having de-Broglie wavelength

λ

is (

h =

Planck's constant,

m =

mass of electron)

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature

T

(Kelvin) and mass

m

is:

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

An electron of mass

m

with an initial velocity

\vec{V} = V_{0} \hat{i} (V_{0} > 0)

enters in an electric field

\vec{E} = {-E}_{0} \hat{i} (E_{0} > 0

and is a constant

)

t = 0

. If

λ_{0}

is its de-Broglie wavelength initially, then its de-Broglie wavelength at time

t

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

An electron is accelerated through a potential difference of

10,000 V .

Its de Broglie wavelength is (nearly):

(m_{e} = 9 \times 1 0^{- 31} k g)

HARD

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

A particle

' P'

is formed due to a completely inelastic collision of particles

' x'

and

' y'

having de-Broglie wavelengths

' λ_{x}'

and

' λ_{y}'

respectively. If

x

and

y

were moving in opposite directions, then the de-Broglie wavelength of

' P'

is:

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

A plane electromagnetic wave having a frequency

f = 23.9 G H z

propagates along the positive

z -

direction in free space. The peak value of the Electric Field is

60 V / m .

Which among the following is the acceptable magnetic field component in the electromagnetic wave?

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

If an electron and a proton have the same de-Broglie wavelength, then the kinetic energy of the electron is

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of

7.5 \times 10^{- 12} m,

the minimum electron energy required is close to:

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Wave Nature of Matter

If the kinetic energy of a moving particle is

E

, then the de-Broglie wavelength is

The de-Broglie wavelength L associated with an elementary particle of linear momentum p is best represented by the graph

Important Questions on Dual Nature of Radiation and Matter

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The de-Broglie wavelength $L$ associated with an elementary particle of linear momentum $p$ is best represented by the graph