Dual Nature Of Radiation And Matter | Physics JEE previous year questions with Solutions

Q 1 :

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{- 4} N$ . If 360 $W . C m^{2}$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is [2024]

$0.02$ $m^{2}$
$0.2$ $m^{2}$
$20$ $m^{2}$
$0.1$ $m^{2}$

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(1)

$Radiation force, F = \frac{I A}{c} \Rightarrow A = \frac{F c}{I}$

$A = \frac{2.4 \times 10^{- 4} \times 3 \times 10^{8}}{360 \times 10^{4}} = \frac{2.4}{120} = 0.02 m^{2}$

Q 2 :

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $6 \times 10^{8} W / m^{2}$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $= 3 \times 10^{8} m / s$ ) [2024]

$36 N m^{- 2}$
$18 N m^{- 2}$
$6 N m^{- 2}$
$2 N m^{- 2}$

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(3)

$Radiation pressure = \frac{I}{V}$

$= \frac{I \cdot μ}{c} = \frac{6 \times 10^{8} \times 3}{3 \times 10^{8}} = 6 {N / m}^{2}$

Q 3 :

Two sources of light emit with a power of 200 W. The ratio of the number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be [2024]

3 : 5
1 : 5
5 : 3
1 : 3

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(1)

$Let n_{1} and n_{2} a r e number of photons emitted by sources per second .$

$n_{1} \times \frac{h c}{λ_{1}} = 200$

$n_{2} \times \frac{h c}{λ_{2}} = 200$

$\frac{n_{1}}{n_{2}} = \frac{λ_{1}}{λ_{2}} = \frac{300}{500} = \frac{3}{5}$

Q 4 :

Monochromatic light of frequency $6 \times 10^{14} H z$ is produced by a laser. The power emitted is $2 \times 10^{- 3} W$ . How many photons per second, on an average, are emitted by the source? [2024]

(Given $h = 6.63 \times 10^{- 34}$ Js)

$9 \times 10^{18}$
$6 \times 10^{15}$
$5 \times 10^{15}$
$7 \times 10^{16}$

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(3)

$Power P = 2 \times 10^{- 3} W$

$Energy E = h ν = 6.63 \times 10^{- 34} \times 6 \times 10^{14}$

$∴ n = \frac{P}{E} = \frac{2 \times 10^{- 3}}{6.63 \times 10^{- 34} \times 6 \times 10^{14}}$

$n = 5 \times 10^{15}$

Q 5 :

In the Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by the hydrogen atom when excited to the first excitation level is ___ nm.

(Given $h c = 1245 e V n m, e = 1.6 \times 10^{- 19} C$ ) [2024]

(122) $10.2 eV = \frac{h c}{λ} \Rightarrow λ = \frac{1245 eV - nm}{10.2 eV} = 122.06 n m$

Q 6 :

If the total energy transferred to a surface in time $t$ is $6.48 \times 10^{9} J$ , then the magnitude of the total momentum delivered to this surface for complete absorption will be [2024]

$2.46 \times 10^{- 3} kgm / s$
$2.16 \times 10^{- 3} kgm / s$
$1.58 \times 10^{- 3} kgm / s$
$4.32 \times 10^{- 3} kgm / s$

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(2)

Energy transferred in time $' t' = 6.48 \times 10^{5} J$

$Power \Rightarrow P = \frac{6.48 \times 10^{5}}{t}$

For complete absorption

$Pressure = \frac{I}{C} = \frac{Energy}{t . A . C}$

$(Pressure \times A) = \frac{Energy}{time \times C}$

$Force = \frac{Energy}{time \times C}$

$Change in momentum = \frac{Energy}{time \times C}$

So $Momentum delivered = \frac{Energy}{C}$

$= \frac{6.48 \times 10^{5}}{3 \times 10^{8}} = 2.16 \times 10^{- 3} kg m/s$

Q 7 :

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed 2 m away from it, is [2025]

$1.5 \times 10^{- 8} Pascals$
0
$6 \times 10^{- 8} Pascals$
$3 \times 10^{- 8} Pascals$

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(3)

$P_{rad} = \frac{2 I}{c}$

Where $I$ = intensity at surface

c = Speed of light

$I = \frac{Power}{Area} = \frac{450}{4 π r^{2}} = \frac{450}{4 π \times 4} = \frac{450}{16 π}$

$P_{rad} = \frac{2 \times 450}{16 π \times 3 \times 10^{8}} = \frac{150}{8 π \times 10^{8}}$

$= 5.97 \times 10^{- 8} \approx 6 \times 10^{- 8} Pascals$

Q 8 :

A small mirror of mass m is suspended by a massless thread of length $l$ . Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity) [2025]

$θ = \frac{3 E}{4 m c \sqrt{g l}}$
$θ = \frac{E}{m c \sqrt{g l}}$
$θ = \frac{E}{2 m c \sqrt{g l}}$
$θ = \frac{2 E}{m c \sqrt{g l}}$

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(4)

Force due to beam assuming complete reflection

$F = \frac{2 P}{c} = \frac{2}{c} \frac{d E}{d t}$ ; P is power

So change in momentum of mirror.

$m (v - 0) = \int F d t = \frac{2}{c} \int d E = \frac{2 E}{c}$ ... (i)

Now using work energy theorem

$W_{g} = △ k$

$- m g l (1 - \cos θ) = 0 - \frac{1}{2} m v^{2}$

$g l (2 \sin^{2} \frac{θ}{2}) = \frac{v^{2}}{2}$

as $θ$ is small

$g l 2 {(\frac{θ}{2})}^{2} = \frac{1}{2} \frac{4 E^{2}}{m^{2} c^{2}}$ from eq. (i)

$g l θ^{2} = \frac{4 E^{2}}{m^{2} c^{2}} \Rightarrow θ = \frac{2 E}{m c \sqrt{g l}}$

Q 9 :

The ratio of the power of a light source $S_{1}$ to that the light source $S_{2}$ is 2. $S_{1}$ is emitting $2 \times 10^{15}$ photons per second at 600 nm. If the wavelength of the source $S_{2}$ is 300 nm, then the number of photons per second emitted by $S_{2}$ is _____ $\times 10^{14}$ . [2025]

(5)

Since power emitted by a source is given as

$P = \frac{Total energy emitted}{time}$

$= \frac{(Energy of photon) \times Number of photons (N)}{t}$

$\frac{P_{1}}{P_{2}} = \frac{(E_{1}) n_{1}}{(E_{2}) n_{2}} = \frac{(\frac{h c}{λ_{1}}) n_{1}}{(\frac{h c}{λ_{2}}) n_{2}}$

$\frac{P_{1}}{P_{2}} = (\frac{λ_{2}}{λ_{1}}) \frac{n_{1}}{n_{2}}$

Substituting the given values

$2 = (\frac{300}{600}) \times \frac{2 \times 10^{15}}{n_{2}}$

$n_{2} = \frac{1}{2} \times 10^{15} = 5 \times 10^{14} Photons / \sec$

Q 10 :

A small object at rest absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed of light is $3 \times 10^{8}$ m/s, the momentum of the object becomes equal to [2023]

$0.5 \times 10^{- 17}$ kg m/s
$2 \times 10^{- 17}$ kg m/s
$3 \times 10^{- 17}$ kg m/s
$1 \times 10^{- 17}$ kg m/s

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(2)

$Momentum p = \frac{Energy}{C} = \frac{Power \times time}{C}$

$p = \frac{(20 \times 10^{- 3} W) (300 \times 10^{- 9} s)}{3 \times 10^{8} m/s} = 2 \times 10^{- 17} kg-m/s$

Q 11 :

A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is [2023]

$\frac{1}{2 π} \frac{W}{m^{2}}$
$\frac{1}{40 π} \frac{W}{m^{2}}$
$\frac{1}{10 π} \frac{W}{m^{2}}$
$\frac{1}{20 π} \frac{W}{m^{2}}$

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(2)

$I_{E F} = \frac{1}{2} \times \frac{5}{4 π \times 5^{2}} = \frac{1}{40 π} {W/m}^{2}$

Q 12 :

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of 24 W. The radius of curvature of hemisphere is 10 cm and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is ____ $\times 10^{- 8}$ N. [2023]

(4)

$Force = \int P d A \cos θ$

$= \frac{2 I}{C} \int d A \cos θ = \frac{2 I}{C} π R^{2} = 2 \frac{p_{0}}{4 π R^{2}} \cdot \frac{π R^{2}}{C}$

$= \frac{p_{0}}{2 C} = \frac{24}{2 \times 3 \times 10^{8}} = 4 \times 10^{- 8} N$

Q 13 :

A photoemissive substance is illuminated with a radiation of wavelength $λ_{i}$ so that it releases electrons with de-Broglie wavelength $λ_{e}$ . The longest wavelength of radiation that can emit photoelectron is $λ_{0}$ . Expression for de-Broglie wavelength is given by ( $m$ = mass of the electron, $h$ = Planck's constant and $c$ = speed of light) [2025]

$λ_{e} = \sqrt{\frac{h λ_{0}}{2 m c}}$
$λ_{e} = \sqrt{\frac{h λ_{i}}{2 m c}}$
$λ_{e} = \frac{h}{\sqrt{2 m c (\frac{1}{λ_{i}} - \frac{1}{λ_{0}})}}$
$λ_{e} = \sqrt{\frac{h}{2 m c (\frac{1}{λ_{i}} - \frac{1}{λ_{0}})}}$

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(4)

Q 14 :

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is __________.

$(Given : h = 6.63 \times 10^{- 34} J \cdot s and 𝑐 = 3 \times 10^{8} m / s)$ [2026]

$2 \times 10^{16}$
$5 \times 10^{16}$
$5 \times 10^{15}$
$10 \times 10^{15}$

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(1)

$P = \frac{n h c}{λ}$

$6 \times 10^{- 3} = \frac{n \times 6.63 \times 10^{- 34} \times 3 \times 10^{8}}{663 \times 10^{- 9}}$

$n = 2 \times 10^{16} photons$

Topic Question Set

Q 1 :

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{- 4} N$ . If 360 $W . C m^{2}$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is [2024]

Q 2 :

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $6 \times 10^{8} W / m^{2}$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $= 3 \times 10^{8} m / s$ ) [2024]

Q 3 :

Two sources of light emit with a power of 200 W. The ratio of the number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be [2024]

Q 4 :

Monochromatic light of frequency $6 \times 10^{14} H z$ is produced by a laser. The power emitted is $2 \times 10^{- 3} W$ . How many photons per second, on an average, are emitted by the source? [2024]

(Given $h = 6.63 \times 10^{- 34}$ Js)

Q 5 :

In the Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by the hydrogen atom when excited to the first excitation level is ___ nm.

(Given $h c = 1245 e V n m, e = 1.6 \times 10^{- 19} C$ ) [2024]

Q 6 :

If the total energy transferred to a surface in time $t$ is $6.48 \times 10^{9} J$ , then the magnitude of the total momentum delivered to this surface for complete absorption will be [2024]

Q 7 :

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed 2 m away from it, is [2025]

Q 8 :

A small mirror of mass m is suspended by a massless thread of length $l$ . Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity) [2025]

Q 10 :

A small object at rest absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed of light is $3 \times 10^{8}$ m/s, the momentum of the object becomes equal to [2023]

Q 11 :

A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is [2023]

(4)

Q 14 :

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is __________.

$(Given : h = 6.63 \times 10^{- 34} J \cdot s and 𝑐 = 3 \times 10^{8} m / s)$ [2026]

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Topic Question Set

Q 1 : Average force exerted on a non-reflecting surface at normal incidence is 2.4×10-4N. If 360 W.Cm2 is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is [2024]

Q 2 : An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity 6×108W/m2 falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space =3×108m/s) [2024]

Q 3 : Two sources of light emit with a power of 200 W. The ratio of the number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be [2024]

Q 4 : Monochromatic light of frequency 6×1014Hz is produced by a laser. The power emitted is 2×10-3W. How many photons per second, on an average, are emitted by the source? [2024] (Given h=6.63×10-34 Js)

Q 5 : In the Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by the hydrogen atom when excited to the first excitation level is ___ nm. (Given hc=1245eVnm, e=1.6×10-19C) [2024]

Q 6 : If the total energy transferred to a surface in time t is 6.48×109J, then the magnitude of the total momentum delivered to this surface for complete absorption will be [2024]

Q 7 : The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed 2 m away from it, is [2025]

Q 8 : A small mirror of mass m is suspended by a massless thread of length l. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity) [2025]

Q 9 : The ratio of the power of a light source S1 to that the light source S2 is 2. S1 is emitting 2×1015 photons per second at 600 nm. If the wavelength of the source S2 is 300 nm, then the number of photons per second emitted by S2 is _____ ×1014. [2025]

Q 10 : A small object at rest absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed of light is 3×108m/s, the momentum of the object becomes equal to [2023]

Q 11 : A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is [2023]

(4)

Q 14 : Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is __________. (Given: h=6.63×10−34J·s and 𝑐=3×108m/s) [2026]

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Q 1 :

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{- 4} N$ . If 360 $W . C m^{2}$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is [2024]

Q 2 :

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $6 \times 10^{8} W / m^{2}$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $= 3 \times 10^{8} m / s$ ) [2024]

Q 3 :

Two sources of light emit with a power of 200 W. The ratio of the number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be [2024]

Q 4 :

Monochromatic light of frequency $6 \times 10^{14} H z$ is produced by a laser. The power emitted is $2 \times 10^{- 3} W$ . How many photons per second, on an average, are emitted by the source? [2024]

(Given $h = 6.63 \times 10^{- 34}$ Js)

Q 5 :

In the Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by the hydrogen atom when excited to the first excitation level is ___ nm.

(Given $h c = 1245 e V n m, e = 1.6 \times 10^{- 19} C$ ) [2024]

Q 6 :

If the total energy transferred to a surface in time $t$ is $6.48 \times 10^{9} J$ , then the magnitude of the total momentum delivered to this surface for complete absorption will be [2024]

Q 7 :

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed 2 m away from it, is [2025]

Q 8 :

A small mirror of mass m is suspended by a massless thread of length $l$ . Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror (c = speed of light in vacuum and g = acceleration due to gravity) [2025]

Q 10 :

A small object at rest absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed of light is $3 \times 10^{8}$ m/s, the momentum of the object becomes equal to [2023]

Q 11 :

A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is [2023]

Q 14 :

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is __________.

$(Given : h = 6.63 \times 10^{- 34} J \cdot s and 𝑐 = 3 \times 10^{8} m / s)$ [2026]