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An $α$ -particle and a proton are accelerated from rest, by a potential difference of $100 V$ . After this, their de-Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}}$ , to the nearest integer, is

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Important Questions on Dual Nature of Radiation and Matter

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

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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

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}

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 de-Broglie wavelength associated with the electron in the $n = 4$ level is:

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}

MEDIUM

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:

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?

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,

EASY

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

Which of the following figures represent the variation of particle momentum and the associated de-Broglie wavelength?

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:

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

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)

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

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:

MEDIUM

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

If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is:

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:

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

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

An electron of mass m and a photon have same energy

E.

The ratio of de-Broglie wavelengths associated with them is:
(

c

being velocity of light)

An α-particle and a proton are accelerated from rest, by a potential difference of 100 V. After this, their de-Broglie wavelengths are λα and λp, respectively. The ratio λpλα, to the nearest integer, is

Important Questions on Dual Nature of Radiation and Matter

Learn and Prepare for any exam you want !

An $α$ -particle and a proton are accelerated from rest, by a potential difference of $100 V$ . After this, their de-Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}}$ , to the nearest integer, is