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Dual Nature of Matter and Radiation

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JEE Advanced 1991

LEVELJEE Advanced

A monochromatic point source $S$ radiating wavelength $6000 \overset{˚}{A}$ , with power $2 W$ , an aperture $A$ of diameter $0.1 m$ and a large screen $S C$ are placed as shown in figure. A photoemissive detector $D$ of surface area $0.5 cm^{2}$ is placed at the centre of the screen. The efficiency of the detector for the photoelectron generation per incident photon is $0.9$ . (a) Calculate the photon flux at (per unit area per unit time) the centre of the screen and the photocurrent in the detector. (b) If the concave lens $L$ of focal length $0.6 m$ is inserted in the aperture as shown, find the new values of photon flux and photocurrent. Assume a uniform average transmission of $80%$ from the lens. (c) If the work function of the photoemissive surface is $1 eV$ , calculate the values of the stopping potential in the two cases (without and with the lens in the aperture).

JEE Advanced 1995

LEVELJEE Advanced

In a photoelectric effect set-up a point of light of power $3.2 \times 1 0^{- 3}$ W emits monoenergetic photons of energy $5.0$ eV. The source is located at a distance of $0.8$ m from the centre of a stationary metallic sphere of work function $3.0$ eV and of radius $8.0 \times 1 0^{- 3}$ m. The efficiency of photoelectrons emission is one for every $1 0^{6}$ incident photons. Assume that the sphere is isolated and initially neutral and that photoelectrons are instantly swept away after emission. (a) Calculate the number of photoelectrons emitted per second. (b) Find the ratio of the wavelength of incident light to the de-Broglie wavelength of the fastest photoelectrons emitted. (c) It is observed that the photoelectrons emission stops at a certain time $t$ after the light source is switched on why ? (d) Evaluate the time $t$ .

JEE Advanced 2004

LEVELJEE Advanced

Wavelengths belonging to Balmer series lying in the range of $450 nm$ to $750 nm$ were used to eject photoelectrons from a metal surface whose work function is $2.0 eV$ . Find (in eV) the maximum kinetic energy of the emitted photoelectrons. (Take $h c = 1242 eV nm$ .)

JEE Advanced 1997

LEVELJEE Advanced

Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with nodes at each of the atomic sites. It is found that one such standing wave is formed if the distance $d$ between the atoms of the array is $2 \overset{˚}{A}$ . A similar standing wave is again formed if $d$ is increased to $2.5 \overset{˚}{A}$ but not for any intermediate value of $d$ . Find the energy of the electron in eV and the least value of $d$ for which the standing wave of the type described above can form.

JEE Advanced 2011

LEVELJEE Advanced

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $A \times 1 0^{Z}$ (where $1 < A < 10$ ). The value of $Z$ is

LEVELJEE Advanced

Electrons in hydrogen-like atom ( $Z = 3$ ) make transitions from the fifth to the fourth orbit and from the fourth to the third orbit. The resulting radiations are incident normally on a metal plate and eject photoelectrons. The stopping potential for the photoelectrons ejected by the shorter wavelength is $3.95 V$ . Calculate the work function of the metal, and the stopping potential for the photoelectrons ejected by the longer wavelength (Rydberg's constant $= 1.094 \times 1 0^{7} m^{- 1}$ )

JEE Advanced 2002

LEVELJEE Advanced

Two metallic plates $A$ and $B$ each of area $5 \times 1 0^{- 4} m^{2}$ , are placed parallel to each other at separation of $1 cm$ . Plate $B$ carries a positive charge of $33.7 \times 1 0^{- 12} C$ . A monochromatic beam of light, with photons of energy $5 eV$ each, starts falling on plate $A$ at $t = 0$ so that $1 0^{16}$ photons fall on it per square metre per second. Assume that one photoelectron is emitted for every $1 0^{6}$ incident photons. Also assume that all the emitted photoelectrons are collected by plate $B$ and the work function of plate $A$ remains constant at the value $2 eV$ . Determine (a) the number of photoelectrons emitted up to $t = 10 s$ , (b) the magnitude of the electric field between the plates $A$ and $B$ at $t = 10 s$ and (c) the kinetic energy of the most energetic photoelectrons emitted at $t = 10 s$ when it reaches plate $B$ . Neglect the time taken by the photoelectron to reach plate $B$ . (Take $ε_{0} = 8.85 \times 1 0^{- 12} C^{2} / N-m^{2}$ ).

JEE Advanced 2018

LEVELJEE Advanced

In a photoelectric experiment, a parallel beam of monochromatic light with power of $200 W$ is incident on a perfectly absorbing cathode of work function $6.25 eV$ . The frequency of light is just above the threshold frequency, so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is $100%$ . A potential difference of $500 V$ is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force $F = n \times 1 0^{- 4} N$ due to the impact of the electrons. The value of $n$ is ........... . (Take mass of the electron, $m_{e} = 9 \times 1 0^{- 31} kg$ and $1 eV = 1.6 \times 1 0^{- 19} J$ )

JEE Advanced 2019

LEVELJEE Advanced

A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular frequency $Ω$ such that $\frac{4 π M Ω}{h} = 1 0^{24} m^{- 2}$ with $h$ as Planck's constant. $N$ photons of wavelength $λ = 8 π \times 1 0^{- 6} m$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1 μ m$ . If the value of $N$ is $x \times 1 0^{12}$ , then the value of $x$ is_______. [Consider the spring as massless]

JEE Main 2014

LEVELJEE Advanced

The radiation corresponding to $3 \to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3 \times 1 0^{- 4}$ T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to

The radiation corresponding to $3 \to 2$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of $5 \times 1 0^{- 4} T$ . Assume that the radius of the largest circular path followed by these electrons is $7 mm$ , the work-function of the metal is (Take, mass of electron $= 9.1 \times 1 0^{- 31} kg$ )

(A)

1.36 eV

(B)

1.88 eV

(C)

0.16 eV

(D)

0.82 eV

JEE Advanced 1989

LEVELJEE Advanced

A beam of light has three wavelengths $4144 \overset{˚}{A}$ , $4972 \overset{˚}{A}$ and $6216 \overset{˚}{A}$ with a total intensity of $3.6 \times 1 0^{- 3} W m^{- 2}$ equally distributed amongst the three wavelengths. The beam falls normally on an area $1.0 cm^{2}$ of a clean metallic surface of work function $2.3 eV$ . Assume that there is no loss of light by reflection and that each energetically capable photon ejects one electron. Calculate the number of photoelectrons liberated in two seconds.

JEE Advanced 2017

LEVELJEE Advanced

A photoelectric material having work-function $ϕ_{0}$ is illuminated with light of wavelength $λ (λ < \frac{h c}{ϕ _{0}})$ . The fastest photoelectron has a de-Broglie wavelength $λ_{d}$ . A change in wavelength of the incident light by $Δ λ$ results in a change $Δ λ_{d}$ in $λ_{d}$ . Then, the ratio $\frac{Δ λ _{d}}{Δ λ}$ is proportional to

(A)

\frac{λ _{d}^{2}}{λ ^{2}}

(B)

\frac{λ _{d}}{λ}

(C)

\frac{λ _{d}^{3}}{λ}

(D)

\frac{λ _{d}^{3}}{λ ^{2}}

JEE Advanced 2006

LEVELJEE Advanced

The graph between $1/ λ$ and stopping potential ( $V$ ) of three metals having work functions $ϕ_{1}, ϕ_{2}$ and $ϕ_{3}$ in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct ? (Here, $λ$ is the wavelength of the incident ray).

* Multiple Correct Options

(A)

Ratio of work functions

ϕ_{1} : ϕ_{2} : ϕ_{3} = 1 : 2 : 4

(B)

Ratio of work functions

ϕ_{1} : ϕ_{2} : ϕ_{3} = 4 : 2 : 1

(C)

tan θ

is directly proportional to

h c / e

, where

h

is Planck's constant and

c

is the speed of light

(D)

The violet colour light can eject photoelectrons from metals 2 and 3

LEVELJEE Advanced

Ultraviolet light of wavelengths $800 \overset{˚}{A}$ and $700 \overset{˚}{A}$ when allowed to fall on hydrogen atoms in their ground state is found to liberate electrons with kinetic energy $1.8 eV$ and $4.0 eV$ respectively. Find the value of Planck's constant.

JEE Advanced 2009

LEVELJEE Advanced

Comprehension Passage

When a particle is restricted to move along

x

-axis between

x = 0

and

x = a

, where

a

is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends

x = 0

and

x = a

. The wavelength of this standing wave is related to the linear momentum

p

of the particle according to the de-Broglie relation. The energy of the particle of mass

m

is related to its linear momentum as

E = \frac{p ^{2}}{2 m}

. Thus, the energy of the particle can be denoted by a quantum number

n

taking values

1, 2, 3, \dots (n = 1

, called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving in the line

x = 0

x = a

. [Take

h = 6.6 \times 1 0^{- 34}

Js and

e = 1.6 \times 1 0^{- 19}

Question 1:

The allowed energy for the particle for a particular value of $n$ is proportional to

(A)

a^{- 2}

(B)

a^{- 3/2}

(C)

a^{- 1}

(D)

a^{2}

Question 2:

If the mass of the particle is $m = 1.0 \times 1 0^{- 30}$ kg and $a = 6.6$ nm, the energy of the particle in its ground state is closest to

(A)

0.8

meV

(B)

8

meV

(C)

80

meV

(D)

800

meV

Question 3:

The speed of the particle that can take discrete values is proportional to

(A)

n^{- 3/2}

(B)

n^{- 1}

(C)

n^{1/2}

(D)

n

JEE Advanced 2013

LEVELJEE Advanced

A proton is fired from very far away towards a nucleus with charge $Q = 120 e$ , where $e$ is the electronic charge. It makes a closest approach of $10 fm$ to the nucleus. The de-Broglie wavelength (in units of fm) of the proton at its start is [Take the proton mass, $m_{p} = (5/3) \times 1 0^{- 27} kg$ ; $h = 6.63 \times 1 0^{- 34} J-s$ ; $e = 1.6 \times 1 0^{- 19} C$ ; $\frac{1}{4 π ε _{0}} = 9 \times 1 0^{9} m/F$ ; $1 fm = 1 0^{- 15} m$ ]

JEE Main 2009

LEVELJEE Advanced

Photoelectric effect experiments are performed using three different metal plates $p, q$ and $r$ having work functions $ϕ_{p} = 2.0$ eV, $ϕ_{q} = 2.5$ eV and $ϕ_{r} = 3.0$ eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct $I - V$ graph for the experiment is

Light of wavelength $λ_{ph}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $ϕ$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. A potential difference $V$ is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is $λ_{e}$ , which of the following statements(s) is (are) true?

* Multiple Correct Options

(A)

λ_{e}

increases at the same rate as

λ_{ph}

for

λ_{ph} < \frac{h c}{ϕ}

(B)

λ_{e}

is approximately halved, if

d

is doubled

(C)

λ_{e}

decreases with increase in

ϕ

and

λ_{ph}

(D)

For large potential difference (

V >> \frac{ϕ}{e}

λ_{e}

is approximately halved if

V

is made four times.

JEE Advanced 2022

LEVELJEE Advanced

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $6.0 V$ . This potential drops to $0.6 V$ if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the wavelength of the first source and the work function of the metal, respectively? [Take $\frac{h c}{e} = 1.24 \times 1 0^{- 6} Jm C^{- 1}$ ]

(A)

1.72 \times 1 0^{- 7} m, 1.20 eV

(B)

1.72 \times 1 0^{- 7} m, 5.60 eV

(C)

3.78 \times 1 0^{- 7} m, 5.60 eV

(D)

3.78 \times 1 0^{- 7} m, 1.20 eV

Micro-Topic Strategy Matrix

Photon Theory of Light

Matter Waves and de Broglie Relation

Photoelectric Effect

Chapter Elite-20 Challenge Zone

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The allowed energy for the particle for a particular value of n is proportional to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the mass of the particle is m=1.0×10−30 kg and a=6.6 nm, the energy of the particle in its ground state is closest to

The speed of the particle that can take discrete values is proportional to

The allowed energy for the particle for a particular value of $n$ is proportional to

If the mass of the particle is $m = 1.0 \times 1 0^{- 30}$ kg and $a = 6.6$ nm, the energy of the particle in its ground state is closest to