Match list-I (Fundamental Experiment) with List-II (its conclusion) and select the correct option from the choices given below the list: List-I List-II A Franck-Hertz Experiment (i) Particle nature of light B Photo-electric experiment (ii) Discrete energy levels of the atom C Davison-Germer Experiment (iii) Wave nature of electron (iv) Structure of atom

A - i i ; B - i ; C - ( i i i )

A - i v ; B - i i i ; C - ( i i )

A - i ; B - i v ; C - ( i i i )

A - i i ; B - i v ; C - ( i i i )

MEDIUM

Earn 100

On the basis of de Broglie hypothesis, obtain the relation for wavelength of an electron accelerated by a p.d of $' V'$ volt.

Important Questions on Dual Nature of Radiation and Matter

HARD

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:

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:

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:

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)

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

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

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

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

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)

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

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 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

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

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}

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

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

Match list-I (Fundamental Experiment) with List-II (its conclusion) and select the correct option from the choices given below the list:

	List-I		List-II
A	Franck-Hertz Experiment	(i)	Particle nature of light
B	Photo-electric experiment	(ii)	Discrete energy levels of the atom
C	Davison-Germer Experiment	(iii)	Wave nature of electron
		(iv)	Structure of atom

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

On the basis of de Broglie hypothesis, obtain the relation for wavelength of an electron accelerated by a p.d of 'V' volt.

Important Questions on Dual Nature of Radiation and Matter

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On the basis of de Broglie hypothesis, obtain the relation for wavelength of an electron accelerated by a p.d of $' V'$ volt.