Dual Nature of Radiation and Matter

Class 12

16 previous-year questions from this chapter every option and the correct answer, free · where the marks are

1. Photoelectric effect and Einstein's equation

Exam focus: Increasing light intensity increases the number of photoelectrons, not their maximum kinetic energy — that depends only on frequency, KEmax = hν − φ — and below the threshold frequency, no electrons come out no matter how bright the light is.

Photoelectric Effect — Part 1 (Dual Nature of Radiation and Matter)

Physics Wallah - Alakh Pandey

Stopping potential, threshold frequency and Einstein's photoelectric equation built up from Hertz and Lenard's observations, not just handed to you.

PhysicsNEET 2025show ▾

Which of the following options (graphs A–D shown) represent the variation of photoelectric current with the property of light shown on the

x

-axis?

Question 38 as printed in the NEET 2025 booklet

A.A only✓
B.A and C
C.A and D
D.B and D

Solution

Above the threshold frequency the photoelectric current is proportional to the intensity (graph A, straight line through the origin) and is independent of frequency, so B, C and D are wrong. A only.

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PhysicsNEET 2024show ▾

If

c

is the velocity of light in free space, the correct statements about a photon among the following are: A. The energy of a photon is

E = h ν

. B. The velocity of a photon is

c

. C. The momentum of a photon is

p = \frac{h ν}{c}

. D. In a photon–electron collision, both total energy and total momentum are conserved. E. A photon possesses positive charge. Choose the correct answer from the options given below:

A.A, B, C and D only✓
B.A, C and D only
C.A, B, D and E only
D.A and B only

Solution

A photon has energy $h ν$ , moves at $c$ , carries momentum $p = h ν / c$ , and photon–electron collisions conserve both energy and momentum. A photon is uncharged, so E is false. Hence A, B, C and D only.

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PhysicsNEET 2023show ▾

The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of

V

volts is proportional to:

A. $V$
B. $\frac{1}{V}$ ✓
C. $\frac{1}{V}$
D. $V^{2}$

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PhysicsNEET 2023show ▾

The work functions of caesium (Cs), potassium (K) and sodium (Na) are 2.14 eV, 2.30 eV and 2.75 eV respectively. If the incident electromagnetic radiation has an energy of 2.20 eV, which of these photosensitive surfaces may emit photoelectrons?

A.Cs only✓
B.Both Na and K
C.K only
D.Na only

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PhysicsNEET 2022show ▾

When two monochromatic lights of frequency

ν

and

\frac{ν}{2}

are incident on a photoelectric metal, their stopping potentials become

\frac{V _{s}}{2}

and

V_{s}

respectively. The threshold frequency for this metal is:

A. $\frac{3}{2} ν$ ✓
B. $2 ν$
C. $3 ν$
D. $\frac{2}{3} ν$

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PhysicsNEET 2021show ▾

The number of photons per second, on an average, emitted by a source of monochromatic light of wavelength 600 nm, when it delivers a power of

3.3 \times 1 0^{- 3}

watt, will be (

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

J s):

A. $1 0^{18}$
B. $1 0^{17}$
C. $1 0^{16}$ ✓
D. $1 0^{15}$

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PhysicsNEET 2020show ▾

The energy required to break one bond in DNA is

1 0^{- 20}

J. This value in eV is nearly:

A.6
B.0.6
C.0.06✓
D.0.006

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PhysicsNEET 2020show ▾

Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and the intensity is doubled?

A.Doubled
B.Four times
C.One-fourth
D.Zero✓

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PhysicsNEET 2020show ▾

Light with an average flux of

20 W/c m^{2}

falls on a non-reflecting surface at normal incidence, having surface area

20 c m^{2}

. The energy received by the surface during a time span of 1 minute is:

A. $10 \times 1 0^{3}$ J
B. $12 \times 1 0^{3}$ J
C. $24 \times 1 0^{3}$ J✓
D. $48 \times 1 0^{3}$ J

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2. Matter waves and de Broglie wavelength

Exam focus: Every moving object has a de Broglie wavelength, λ = h/mv, not just electrons — it's simply too small to matter macroscopically. For an electron accelerated through potential V, this gives λ = h/√(2meV), a frequently tested formula in its own right.

Wave Nature of Matter: de Broglie Hypothesis

Physics Wallah - Alakh Pandey

Dedicated lecture on de Broglie's matter-wave hypothesis and wavelength.

PhysicsNEET 2025show ▾

A photon and an electron (mass

m

) have the same energy

E

. The ratio

λ_{photon} / λ_{electron}

of their de Broglie wavelengths is (

c

is the speed of light):

A. $\frac{2 E}{m}$
B. $c 2 m E$
C. $\frac{2 m c ^{2}}{E}$ ✓
D. $\frac{1}{c} \frac{2 E}{m}$

Solution

Photon: $λ_{p} = \frac{h c}{E}$ . Electron: $λ_{e} = \frac{h}{2 m E}$ . Ratio $= \frac{h c}{E} \cdot \frac{2 m E}{h} = c \frac{2 m}{E} = \frac{2 m c ^{2}}{E}$ .

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PhysicsNEET 2025show ▾

The de Broglie wavelength of an electron orbiting in the

n = 2

state of the hydrogen atom is close to (given Bohr radius = 0.052 nm):

A.0.067 nm
B.0.67 nm✓
C.1.67 nm
D.2.67 nm

Solution

In the $n$ th orbit the circumference equals $n$ de Broglie wavelengths: $2 π r_{n} = nλ$ . With $r_{2} = 4 a_{0} = 0.208$ nm: $λ = \frac{2 π \times 0.208}{2} \approx 0.65$ nm $\approx 0.67$ nm.

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PhysicsNEET 2024show ▾

The graph which shows the variation of

\frac{1}{λ ^{2}}

with the kinetic energy

E

of a free particle (where

λ

is its de Broglie wavelength) is: Question 18 as printed in the NEET 2024 booklet

Question 18 as printed in the NEET 2024 booklet

A.Graph (1)
B.Graph (2)
C.Graph (3)✓
D.Graph (4)

Solution

$λ = \frac{h}{2 m E} \Rightarrow \frac{1}{λ ^{2}} = \frac{2 m E}{h ^{2}}$ , which is directly proportional to $E$ : a straight line through the origin.

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PhysicsNEET 2022show ▾

The graph which shows the variation of the de Broglie wavelength (

λ

) of a particle and its associated momentum (

p

) is:

Question 30 as printed in the NEET 2022 booklet

A.Graph (1)✓
B.Graph (2)
C.Graph (3)
D.Graph (4)

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PhysicsNEET 2021show ▾

An electromagnetic wave of wavelength

λ

is incident on a photosensitive surface of negligible work function. If the photoelectron of mass

m

emitted from the surface has de Broglie wavelength

λ_{d}

, then:

A. $λ = (\frac{2 m}{h c}) λ_{d}^{2}$
B. $λ_{d} = (\frac{2 m c}{h}) λ^{2}$
C. $λ = (\frac{2 m c}{h}) λ_{d}^{2}$ ✓
D. $λ = (\frac{2 h}{m c}) λ_{d}^{2}$

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PhysicsNEET 2020show ▾

An electron is accelerated from rest through a potential difference of

V

volt. If the de Broglie wavelength of the electron is

1.227 \times 1 0^{- 2}

nm, the potential difference is:

A.10 V
B. $1 0^{2}$ V
C. $1 0^{3}$ V
D. $1 0^{4}$ V✓

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PhysicsNEET 2019show ▾

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}

kg)

A. $12.2 \times 1 0^{- 13}$ m
B. $12.2 \times 1 0^{- 12}$ m✓
C. $12.2 \times 1 0^{- 14}$ m
D.12.2 nm

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