Cathode rays of velocity ${10^6}{\rm{\;m}}{{\rm{s}}^{ - 1}}$ describe an approximate circular path of radius 1 m in an electric field $300\;{\rm{Vc}}{{\rm{m}}^{ - 1}}.$ If velocity of cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

$1200\;{\rm{Vc}}{{\rm{m}}^{ - 1}}$

$2400{\rm{\;Vc}}{{\rm{m}}^{ - 1}}$

$600\;{\rm{Vc}}{{\rm{m}}^{ - 1}}$

$12000\;{\rm{Vc}}{{\rm{m}}^{ - 1}}$

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NEET • PHYSICS • DUAL NATURE OF RADIATION AND MATTER

Dual nature of radiation and matter practice · Mixed difficulty

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Showing 1-30 of 130 questions

1 Medium

1 of 130

Application +4 | -1

If the Broglie wavelengths associated with a proton and an

\alpha

- particle are equal, then the ratio of velocities of the proton and the

\alpha

- particle will be:

View answer and explanation

Correct option: C

4\mathrm{ }:\mathrm{ }1

Option C (

4\mathrm{ }:\mathrm{ }1

) is correct because the ratio of velocities is inversely proportional to the ratio of masses when de Broglie wavelengths are equal.

2 Medium

2 of 130

Application +4 | -1

If the wavelength of incident light changes from 400 nm to 300 nm, the stopping potential for photoelectrons emitted from a surface becomes approximately

View answer and explanation

Correct option: A

1.0 V greater

Option A (1.0 V greater) is correct because the stopping potential increases when the wavelength of incident light decreases.

3 Hard

3 of 130

Understanding +4 | -1

In photo-electric effect, when graph is plotted for stopping potential versus frequency of incident light, for different metals, then:

View answer and explanation

Correct option: C

The slope is universal constant equal to

(h / e)

Option C (The slope is universal constant equal to

(h / e)

) is correct because the slope of the stopping potential vs. frequency graph is Planck's constant divided by the elementary charge.

4 Hard

4 of 130

Application +4 | -1

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 {10^{ - 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

View answer and explanation

Correct option: B

1.1 eV

Option B (1.1 eV) is correct because it is the work function calculated using the photoelectric effect equation and the given radius of the circular path of the photoelectrons in the magnetic field.

5 Medium

5 of 130

Understanding +4 | -1

The shortest wavelength of

X

-rays emitted from an

X

-ray tube depends on the

View answer and explanation

Correct option: B

Voltage applied to the tube

Option B (Voltage applied to the tube) is correct because the shortest wavelength of X-rays emitted from an X-ray tube is determined by the maximum energy of the electrons, which is directly related to the applied voltage.

6 Medium

6 of 130

Understanding +4 | -1

Planck’s constant has the dimensions of

View answer and explanation

Correct option: D

Angular momentum

Option D (Angular momentum) is correct because Planck's constant has the dimensions of energy multiplied by time, which is equivalent to the dimensions of angular momentum.

7 Medium

7 of 130

Understanding +4 | -1

An electromagnetic radiation has an energy of

13.2\;keV.

Then the radiation belongs to the region of

View answer and explanation

Correct option: D

X-ray

Option D (X-ray) is correct because electromagnetic radiation with an energy of 13.2 keV falls within the X-ray region of the electromagnetic spectrum.

8 Medium

8 of 130

Understanding +4 | -1

The cathode of a photoelectric cell is changed such that the work function changes from

{W_1}

{W_2}\left( {{W_2} > {W_1}} \right).

If the current before and after change are

{I_1}

and

{I_2},

all other conditions remaining unchanged, then (assuming

hv > {W_2}

)

View answer and explanation

Correct option: A

{I_1} = {I_2}

Option A (

{I_1} = {I_2}

) is correct because the current depends on the number of photoelectrons emitted, which is determined by the intensity and frequency of the incident light, not the work function (as long as

hv > W_2

9 Hard

9 of 130

Application +4 | -1

The extent of localisation of a particle is determined roughly by its de Broglie wavelength. If an electron is localized within the nucleus (of size about

10^{-14} \mathrm{~m}

) of an atom, what is its energy?

View answer and explanation

Correct option: A

124.3 \mathrm{~MeV}

Option A (

124.3 \mathrm{~MeV}

) is correct because it is the approximate energy calculated using the uncertainty principle and relativistic energy-momentum relation.

10 Easy

10 of 130

Application +4 | -1

When a metal surface is illuminated by light of wavelength

\lambda

, the stopping potential is

8 \mathrm{~V}

. When the same surface is illuminated by light of wavelength

3 \lambda

, stopping potential is

2 \mathrm{~V}

. The threshold wavelength for this surface is:

View answer and explanation

Correct option: C

9 \lambda

Option C (

9 \lambda

) is correct because it is derived from solving the two photoelectric effect equations simultaneously to find the threshold wavelength.

11 Medium

11 of 130

Application +4 | -1

The de-Broglie wavelength of a neutron at

27^\circ C

\lambda

. What will be its wavelength at

927^\circ C

View answer and explanation

Correct option: A

\lambda /2

Option A (

\lambda /2

) is correct because the de-Broglie wavelength is inversely proportional to the square root of the temperature.

12 Medium

12 of 130

Analyzing +4 | -1

The frequency and intensity of a light source are doubled. Consider the following statements

I. Saturation photocurrent remains almost the same.

II. Maximum kinetic energy of the photoelectrons is doubled.

View answer and explanation

Correct option: C

I is false but II is true.

Option C (I is false but II is true) is correct because saturation photocurrent depends on intensity, and maximum kinetic energy depends on frequency.

13 Medium

13 of 130

Analyzing +4 | -1

The de-Broglie wavelength of an electron,

\alpha

- particle and proton all having the same kinetic energy is respectively given as

{\lambda _e},\;{\lambda _\alpha }\;\;\mathrm{and\;}{\lambda _p}.

Then which of the following is not true?

View answer and explanation

Correct option: A

{\lambda _e} < {\lambda _p}

Option A (

\frac{{{E_e}}}{{{E_p}}} = \frac{v}{{2c}}

) is correct because it relates the kinetic energies of the electron and photon based on their de-Broglie wavelengths and velocities.

14 Medium

14 of 130

Application +4 | -1

In a photoelectric experiment for

4000\;\mathop A\limits^ \circ

incident radiation, the potential difference to stop the ejection is

2V.

If the incident light is changed to

3000\;\mathop A\limits^ \circ ,

then the potential required to stop the ejection of electrons will be

View answer and explanation

Correct option: D

Greater than

2\;V

Option D (Greater than 2 V) is correct because shorter wavelengths correspond to higher energy photons, requiring a greater stopping potential.

15 Easy

15 of 130

Application +4 | -1

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is

25 \%

of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be

View answer and explanation

Correct option: A

\frac{1}{8}

Option A (

\frac{1}{8}

) is correct because the ratio of kinetic energies can be found by comparing the kinetic energy of the electron to the energy of the photon, considering their relationship through de-Broglie wavelength.

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16 Medium

16 of 130

Application +4 | -1

The energy of a photon of light with wavelength

5000\;\mathop A\limits^ \circ

is approximately

2.5\;eV.

This way the energy of an

X

-ray photon with wavelength

1\mathop A\limits^ \circ

would be

View answer and explanation

Correct option: C

2.5 \times 5000\;eV

Option C (

2.5 \times 5000\;eV

) is correct because the energy of a photon is inversely proportional to its wavelength.

17 Medium

17 of 130

Analyzing +4 | -1

The filament current in the electron gun of a coolidge tube is increased while the potential difference used to accelerate the electrons is decreased. As a result, in the emitted radiation

View answer and explanation

Correct option: C

The intensity as well as the minimum wavelength increases

Option C (The intensity as well as the minimum wavelength increases) is correct. Increasing filament current increases intensity, and decreasing accelerating potential increases minimum wavelength.

18 Hard

18 of 130

Remembering +4 | -1

Which of the following is NOT an application of
photodiode?

View answer and explanation

Correct option: D

data profiling

Option D (data profiling) is correct because photodiodes are used for optical signal detection, object counting, and optocouplers, but not for data profiling.

19 Easy

19 of 130

Application +4 | -1

UV light of

4.13 \mathrm{~eV}

is incident on a photosensitive metal surface having work function

3.13 \mathrm{~eV}

. The maximum kinetic energy of ejected photoelectrons will be :

View answer and explanation

Correct option: B

1 \mathrm{~eV}

Option B (1 eV) is correct because the maximum kinetic energy is the difference between the incident photon energy and the work function:

KE_{max} = 4.13 \mathrm{eV} - 3.13 \mathrm{eV} = 1 \mathrm{eV}

20 Medium

20 of 130

Application +4 | -1

What is additional KE that should be given to an electron to reduce de Broglie wavelength from 1 nm to 0.5 nm?

View answer and explanation

Correct option: D

Three times initial value

Option D (Three times initial value) is correct because the kinetic energy is inversely proportional to the square of the de Broglie wavelength.

21 Medium

21 of 130

Remembering +4 | -1

Albert Einstein was awarded Nobel Prize and his work on

View answer and explanation

Correct option: C

Photoelectric effect

Option C (Photoelectric effect) is correct because Albert Einstein was awarded the Nobel Prize for his explanation of the photoelectric effect.

22 Easy

22 of 130

Analyzing +4 | -1

Statement-1: If an electron has the same wavelength as a photon, they have the same energy.
Statement-2: By de-Broglie hypothesis,

p=h / \lambda

for both the electron and the photon.

View answer and explanation

Correct option: D

Statement-1 is false, Statement-2 is true

Option A (

{\lambda _e} < {\lambda _p}

) is not true because the de-Broglie wavelength is inversely proportional to the square root of the mass, and electrons are lighter than protons.

23 Hard

23 of 130

Application +4 | -1

Cathode rays of velocity

{10^6}\mathrm{\;m}{\mathrm{s}^{ - 1}}

describe an approximate circular path of radius 1 m in an electric field

300\;\mathrm{Vc}{\mathrm{m}^{ - 1}}.

If velocity of cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

View answer and explanation

Correct option: C

1200\;\mathrm{Vc}{\mathrm{m}^{ - 1}}

Option C (

1200\mathrm{\;Vc}{\mathrm{m}^{ - 1}}

) is correct because the electric field must be quadrupled to maintain the same circular path when the velocity is doubled.

24 Medium

24 of 130

Remembering +4 | -1

Momentum of a photon of wavelength

\lambda

View answer and explanation

Correct option: A

h/\lambda

Option A is correct because the momentum of a photon is given by p = h/λ, where h is Planck's constant and λ is the wavelength.

25 Easy

25 of 130

Application +4 | -1

1 \mathrm{~mW}

of light of wavelength

456 \mathrm{~nm}

is incident on a cesium surface. If the quantum efficiency of the surface for photoelectric emission is only

0.5 \%

then, the photoelectric current produced (in

\mu \mathrm{A}

) is

View answer and explanation

Correct option: A

1.84

Option A (1.84) is correct because the photoelectric current is calculated based on the quantum efficiency and the number of incident photons.

26 Medium

26 of 130

Remembering +4 | -1

Which of the following metals having highest
work function is

View answer and explanation

Correct option: D

Pt

Option D (

Pt

) is correct because Platinum (Pt) generally has the highest work function among the given metals.

27 Easy

27 of 130

Application +4 | -1

If wave function of a metal is

6.68 \mathrm{eV}

. Find threshold frequency.

View answer and explanation

Correct option: B

1.6 \times 10^{15} \mathrm{~Hz}

Option B (

1.6 \times 10^{15} \mathrm{~Hz}

) is correct because it is calculated using the formula

f = \phi/h

, where

\phi

is the work function and

h

is Planck's constant.

28 Easy

28 of 130

Application +4 | -1

The threshold frequency for a photosensitive metal is

3.3 \times {10^{14}}\,Hz.\,

If light of frequency

8.2 \times {10^{14}}\,Hz

is incident on this metal, the cut-off voltage for the photoelectric emission is nearly

View answer and explanation

Correct option: A

2 V

Option A (2 V) is correct because the cut-off voltage (stopping potential) can be calculated using the photoelectric equation, and it's approximately 2V.

29 Medium

29 of 130

Application +4 | -1

The electron in the hydrogen atom jumps from excited state

\left( {n = 3} \right)

to its ground state

\left( {n = 1} \right)

and the photons thus emitted irradiate a photosensitive material. If the work function of the material is

5.1\,\,\mathrm{eV}

, the stopping potential is estimated to be (the energy of the electron in

{n^{th}}

state

{E_n} = - \frac{{13.6}}{{{n^2}}}\,eV

)

View answer and explanation

Correct option: D

\begin{array}{llllllllllllllllllll} {\mathrm{7}\,\,\mathrm{V}} \end{array}

Option D (7 V) is correct because it is the stopping potential calculated using the energy difference between the excited and ground states and the work function.

30 Medium

30 of 130

Remembering +4 | -1

A stream of fast moving negatively charged particles are called

View answer and explanation

Correct option: A

Cathode rays

Option A (Cathode rays) is correct because cathode rays are streams of fast-moving, negatively charged particles (electrons).

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