Dual Nature of Radiation and Matter

An electron and an alpha particle are accelerated by the same potential difference. Let \({\lambda }_{e}\) and \({\lambda }_{\alpha }\) denote the de Broglie wavelengths of the electron and the alpha particle, respectively, then:

[Re-NEET 2024]

For a metal of work function 6.6 eV , which of the following wavelengths of incident radiation does not give rise to the photoelectric effect ?
(Take Planck's constant as \(6.6\times {10}^{-34}Js\) )

If c is the velocity of light in free space, the correct statements about photon among the following are:
A. The energy of a photon is \(E=h\nu\)
B. The velocity of a photon is c.
C. The momentum of a photon, \(p=\frac{hv}{c}\).
D. In a photon-electron collision, both total energy and total momentum are conserved.
E. Photon possesses positive charges.
Choose the correct answer from the options given below :

[NEET 2024]

An electron and an alpha particle are accelerated by the same potential difference. Let \({\lambda }_{e}\) and \({\lambda }_{\alpha }\) denote the de Broglie wavelengths of the electron and the alpha particle respectively, then:

[Re-NEET 2024]

Match List I with List II :

Choose the correct answer from the options given below:

If \(\phi\) is the work function of photosensitive material in Joules and light of wavelength of numerical value \(\lambda =\frac{hc}{e}\) metre, is incident on it with energy above its threshold value at an instant then the maximum kinetic energy of the photo-electron ejected by it at that instant (Take h-Planck's constant, c-velocity of light in free space) is (in SI units) :

[Re-NEET 2024]

The difference between threshold wavelengths for two metal surfaces \(A\) and \(B\) having work function \(\phi_A=9 eV\) and \(\phi_B=4.5 eV\) in \(nm\) is:
(Given, hc \(=1242 eV nm ) \quad\)

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

An electron of mass \( m \) and magnitude of charge \( |e| \) initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time \( t \) ignoring relativistic effects is:

Assertion: A negative potential is required to stop the photoelectron in a photocell.

Reason: The speed of the electron decreases when a negative potential is applied in a photocell.

(Shift - I Memory Based)

In a photoelectric experiment, increasing the intensity of incident light:

[JEE Main 2021, 27 Aug (Shift 1)]

The threshold frequency of metal is \(f_0\). When the light of frequency \(2 f_0\) is incident on the metal plate, the maximum velocity of photoelectron is \(v_1\). When the frequency of incident radiation is increased to \(5 f_0\), the maximum velocity of photoelectrons emitted is \(v_2\). The ratio of \(v_1\) to \(v_2\) is:

An electron accelerated through a potential difference \(V_1\) has a de-Broglie wavelength of \(\lambda\). When the potential is changed to \(V_2\), its de-Broglie wavelength increases by \(50 \%\). The value of \(\left(\frac{V_1}{V_2}\right)\) is equal to:

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

[NEET 2023]

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 intensity is doubled?

[NEET 2020]

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of \(\lambda\). An alpha particle having certain kinetic energy has the same de-Broglie wavelength \(\lambda\). The ratio of kinetic energy of proton and that of alpha particle is:

[JEE Main 2023, 1 Feb (Shift 1)]

An electromagnetic wave of wavelength \( \lambda \) is incident on a photosensitive surface of negligible work function. If '\(m\)' mass is of photoelectrons emitted from this surface has de-Broglie wavelength \( \lambda_{d} \) then
[NEET 2021]

A proton and an \(\alpha\)-particle are accelerated from rest by \(2 V\) and \(4 V\) potentials, respectively. The ratio of their deBroglie wavelength is:

[JEE Main 2023, 12 Apr (Shift 1)]

An electron is accelerated from rest through a potential difference of \( \mathrm{V} \) volt. If the de Broglie wavelength of the electron is \( 1.227 \times 10^{-2} \mathrm{~nm} \), the potential difference is :

[NEET 2020]

A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is \(2: 1\), the mass of the particle is:

An electron moving with speed \(v\) and a photon moving with speed \(c\), have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is:

[JEE Main 2021, 25 Jul (Shift 2)]

The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 \( \mathrm{nm} \), when it delivers the power of \( 3.3 \times 10^{-3} \) watt will be: \( \left(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}\right) \)

[NEET 2021]

If the ratio of de-Broglie wavelength of an \(\alpha\)-particle and a proton accelerated from rest by the same potential is \(\frac{1}{\sqrt{m}}\), then the value of \(m\) is \(\quad\)

[JEE Main 2023, 29 Jan (Shift 2)]

The wave character of electron was experimentally verified by:

[Re-NEET 2020]

If a source of electromagnetic radiation having power \(15 kW\) produces \(10^{16}\) photons per second, the radiation belongs to a part of spectrum is.(Take Planck constant \(h=6 \times 10^{-34} Js\) )

[JEE Main 2023, 31 Jan (Shift 1)]

The de Broglie wavelength of an electron moving with kinetic energy of \( 144 \mathrm{eV} \) is nearly,

[Re-NEET 2020]

Proton (p) and electron (e) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(\left.m_{ p }=1849 m_{ e }\right)\)

[JEE Main 2023, 8 Apr (Shift 1)]

In a photoelectric experiment ultraviolet light of wavelength \(280 nm\) is used with lithium cathode having work function \(\phi=2.5 eV\). If the wavelength of incident light is switched to \(400 nm\), find out the change in the stopping potential. \(\left(h=6.63 \times 10^{-34} Js , c=3 \times 10^8 ms ^{-1}\right)\)

An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

An electromagnetic wave of wavelength \(\lambda\) is incident on a photosensitive surface of negligible work function. If the photoelectrons of mass m emitted from this surface have de Broglie wavelength \({\lambda }_{1}\) then