Wave Particle Duality

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JEE Advanced 2021

LEVELJEE Main

Consider a helium (He) atom that absorbs a photon of wavelength $330 nm$ . The change in the velocity (in $cm s^{- 1}$ ) of He atom after the photon absorption is ______. (Assume: Momentum is conserved when photon is absorbed. [Use: Planck constant $= 6.6 \times 1 0^{- 34} J s$ , Avogadro number $= 6 \times 1 0^{23} mol^{- 1}$ , Molar mass of He $= 4 g mol^{- 1}$ ]

JEE Main 2019

LEVELJEE Main

Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?

If $p$ is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $λ$ , then for $1.5 p$ momentum of the photoelectron, the wavelength of the light should be (Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

(A)

\frac{4}{9} λ

(B)

\frac{3}{4} λ

(C)

\frac{2}{3} λ

(D)

\frac{1}{2} λ

JEE Main 2021

LEVELJEE Advanced

When light of wavelength $248 nm$ falls on a metal of threshold energy $3.0 eV$ , the de-Broglie wavelength of emitted electrons is ...... $\overset{˚}{A}$ . [Round off to the nearest integer] [Use: $3 = 1.73$ , $h = 6.63 \times 1 0^{- 34} Js$ , $m_{e} = 9.1 \times 1 0^{- 31} kg$ , $c = 3.0 \times 1 0^{8} ms^{- 1}$ , $1 eV = 1.6 \times 1 0^{- 19} J$ ]

JEE Main 2020

LEVELJEE Main

The figure that is not a direct manifestation of the quantum nature of atoms is

If the de-Broglie wavelength of the electron in $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5 π a_{0}$ ( $a_{0}$ is Bohr radius), then the value of $n / Z$ is

The number of photons emitted by a monochromatic (single frequency) infrared range finder of power $1 mW$ and wavelength of $1000 nm$ , in $0.1 second$ is $x \times 1 0^{13}$ . The value of $x$ is ......... . (Nearest integer) ( $h = 6.63 \times 1 0^{- 34} Js, c = 3.00 \times 1 0^{8} ms^{- 1}$ )

JEE Main 2021

LEVELJEE Main

A source of monochromatic radiation of wavelength $400 nm$ provides $1000 J$ of energy in $10$ seconds. When this radiation falls on the surface of sodium, $x \times 1 0^{20}$ electrons are ejected per second. Assume that wavelength $400 nm$ is sufficient for ejection of electron from the surface of sodium metal. The value of $x$ is ...... . (Nearest integer) $(h = 6.626 \times 1 0^{- 34} Js)$

JEE Main 2019

LEVELJEE Main

The de-Broglie wavelength ( $λ$ ) associated with a photoelectron varies with the frequency ( $ν$ ) of the incident radiation as, [ $ν_{0}$ is threshold frequency]

(A)

λ \propto \frac{1}{( ν - ν _{0} ) ^{1/4}}

(B)

λ \propto \frac{1}{( ν - ν _{0} ) ^{3/2}}

(C)

λ \propto \frac{1}{( ν - ν _{0} )}

(D)

λ \propto \frac{1}{( ν - ν _{0} ) ^{1/2}}

JEE Main 2016

LEVELJEE Main

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference $V$ esu. If $e$ and $m$ are charge and mass of an electron, respectively, then the value of $h / λ$ (where, $λ$ is wavelength associated with electron wave) is given by

(A)

2 m e V

(B)

m e V

(C)

2 m e V

(D)

m e V

JEE Main 2021

LEVELJEE Main

A 50 watt bulb emits monochromatic red light of wavelength of $795 nm$ . The number of photons emitted per second by the bulb is $x \times 1 0^{20}$ . The value of $x$ is ......... . [Given, $h = 6.63 \times 1 0^{- 34} Js$ and $c = 3.0 \times 1 0^{8} ms^{- 1}$ ]

JEE Main 2021

LEVELJEE Main

Given below are two statements : Statement I Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen atom. Statement II Bohr's model of hydrogen atom contradicts Heisenberg's uncertainty principle. In the light of the above statements, choose the most appropriate answer from the options given below :

(A)

Statement I is false but statement II is true.

(B)

Statement I is true but statement II is false.

(C)

Both statement I and statement II are false.

(D)

Both statement I and statement II are true.

JEE Main 2019

LEVELJEE Advanced

What is the work function of the metal, if the light of wavelength $4000 \overset{˚}{A}$ generates photoelectron of velocity $6 \times 1 0^{5} ms^{- 1}$ from it? (Mass of electron $= 9 \times 1 0^{- 31} kg$ Velocity of light $= 3 \times 1 0^{8} ms^{- 1}$ Planck's constant $= 6.626 \times 1 0^{- 34} Js$ Charge of electron $= 1.6 \times 1 0^{- 19} JeV^{- 1}$ )

(A)

4.0 eV

(B)

2.1 eV

(C)

0.9 eV

(D)

3.1 eV

JEE Main 2020

LEVELJEE Main

The work function of sodium metal is $4.41 \times 1 0^{- 19}$ J. If photons of wavelength $300$ nm are incident on the metal, the kinetic energy of the ejected electrons will be $(h = 6.63 \times 1 0^{- 34} J s; c = 3 \times 1 0^{8} m/s)$ ............ $\times 1 0^{- 21}$ J.

LEVELJEE Main

A gas absorbs photon of $355 nm$ and emits at two wavelengths. If one of the emission is at $680 nm$ , the other is at

(A)

1035 nm

(B)

325 nm

(C)

743 nm

(D)

518 nm

JEE Main 2021

LEVELJEE Main

The wavelength of electrons accelerated from rest through a potential difference of $40 kV$ is $x \times 1 0^{- 12} m$ . The value of $x$ is ...... (Nearest integer) Given : Mass of electron $= 9.1 \times 1 0^{- 31} kg$ Charge on an electron $= 1.6 \times 1 0^{- 19} C$ Planck's constant $= 6.63 \times 1 0^{- 34} Js$

JEE Main 2021

LEVELJEE Main

Electromagnetic radiation of wavelength $663 nm$ is just sufficient to ionise the atom of metal A. The ionisation energy of metal A in $kJ mol^{- 1}$ is ……… . (Rounded off to the nearest integer) $[h = 6.63 \times 1 0^{- 34} J-s, c = 3.00 \times 1 0^{8} ms^{- 1}, N_{A} = 6.02 \times 1 0^{23} mol^{- 1}]$

JEE Main 2021

LEVELJEE Advanced

An accelerated electron has a speed of $5 \times 1 0^{6} ms^{- 1}$ with an uncertainty of $0.02%$ . The uncertainty in finding its location while in motion is $x \times 1 0^{- 9} m$ . The value of $x$ is ......... . (Nearest integer) [Use mass of electron $= 9.1 \times 1 0^{- 31} kg$ , $h = 6.63 \times 1 0^{- 34} Js$ , $π = 3.14$ ]

JEE Main 2021

LEVELJEE Advanced

A metal surface is exposed to $500 nm$ radiation. The threshold frequency of the metal for photoelectric current is $4.3 \times 1 0^{14} Hz$ . The velocity of ejected electron is ......... $\times 1 0^{5} ms^{- 1}$ . (Nearest integer) [Use $h = 6.63 \times 1 0^{- 34} Js$ , $m_{e} = 9.0 \times 1 0^{- 31} kg$ ]

JEE Main 2021

LEVELJEE Main

A proton and a $Li^{3 +}$ nucleus are accelerated by the same potential. If $λ_{Li}$ and $λ_{p}$ denote the de-Broglie wavelengths of $Li^{3 +}$ and proton respectively, then the value of $\frac{λ _{Li}}{λ _{p}}$ is $x \times 1 0^{- 1}$ . The value of $x$ is ......... . (Rounded off to the nearest integer) (Mass of $Li^{3 +} = 8.3$ mass of proton)

JEE Main 2021

LEVELJEE Main

A ball weighing $10 g$ is moving with a velocity of $90 ms^{- 1}$ . If the uncertainity in its velocity is $5%$ , then the uncertainty in its position is ......... $\times 1 0^{- 33} m$ (Rounded off to the nearest integer). [Given, $h = 6.63 \times 1 0^{- 34} J-s$ ]

Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?

The figure that is not a direct manifestation of the quantum nature of atoms is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the de-Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5πa0​ (a0​ is Bohr radius), then the value of n/Z is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The de-Broglie wavelength (λ) associated with a photoelectron varies with the frequency (ν) of the incident radiation as, [ν0​ is threshold frequency]

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A gas absorbs photon of 355 nm and emits at two wavelengths. If one of the emission is at 680 nm, the other is at

If the de-Broglie wavelength of the electron in $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5 π a_{0}$ ( $a_{0}$ is Bohr radius), then the value of $n / Z$ is

The de-Broglie wavelength ( $λ$ ) associated with a photoelectron varies with the frequency ( $ν$ ) of the incident radiation as, [ $ν_{0}$ is threshold frequency]

A gas absorbs photon of $355 nm$ and emits at two wavelengths. If one of the emission is at $680 nm$ , the other is at