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A proton and an $α$ -particle are accelerated through a potential difference of $100 V$ . The ratio of the wavelength associated with the proton to that associated with an $α$ -particle 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

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

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)

A proton and an α-particle are accelerated through a potential difference of 100 V. The ratio of the wavelength associated with the proton to that associated with an α-particle is :-

Important Questions on Dual Nature of Radiation and Matter

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A proton and an $α$ -particle are accelerated through a potential difference of $100 V$ . The ratio of the wavelength associated with the proton to that associated with an $α$ -particle is :-