Dual Nature Of Radiation And Matter

Electrons of mass m with de Broglie wavelength λ fall on the target in an X-ray tube. The cutoff wavelength (λ₀) of the emitted X-ray is:

An electron of mass m and a photon have the same energy E. The ratio of the de Broglie wavelengths associated with them is (c being the velocity of light):

When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is V/4. The threshold wavelength for the metallic surface is:

Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A if the stopping potential of A relative to C is:

The photoelectric threshold wavelength of silver is 3250 × 10⁻¹⁰ m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536 × 10⁻¹⁰ m is (Given h = 4.14 × 10⁻¹⁵ eV·s and c = 3 × 10⁸ m/s):

The de Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass m is:

When the light of frequency 2ν₀ (where ν₀ is the threshold frequency) is incident on a metal plate, the maximum velocity of electrons emitted is v₁. When the frequency of the incident radiation is increased to 5ν₀, the maximum velocity of electrons emitted from the same plate is v₂. The ratio of v₁ to v₂ is:

An electron of mass m with an initial velocity v = v₀ î (v₀ > 0) enters an electric field E = −E₀ î (E₀ = constant > 0) at t = 0. If λ₀ is its de Broglie wavelength initially, then its de Broglie wavelength at time t is:

A proton and an α-particle are accelerated from rest to the same energy. The de Broglie wavelengths λ_p and λ_α are in the ratio:

The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photoemission from the substance is (approximately):

An electron is accelerated through a potential difference of 10000 V. Its de Broglie wavelength is, (nearly): (mₑ = 9 × 10⁻³¹ kg)

An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227 × 10⁻² nm, the potential difference is:

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?

The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3 × 10⁻³ W will be: (h = 6.6 × 10⁻³⁴ J·s)

An electromagnetic wave of wavelength λ is incident on a photosensitive surface of negligible work function. If a photoelectron of mass m emitted from the surface has de Broglie wavelength λ_d, then:

When two monochromatic lights of frequency ν and ν/2 are incident on a photoelectric metal, their stopping potentials become V_s/2 and V_s respectively. The threshold frequency for this metal is:

The graph which shows the variation of the de Broglie wavelength (λ) of a particle and its associated momentum (p) is:

The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to:

The maximum kinetic energy of the emitted photoelectrons in the photoelectric effect is independent of:

The de Broglie wavelength associated with an electron, accelerated by a potential difference of 81 V, is given by:

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 energy of 2.20 eV, which of these photosensitive surfaces may emit photoelectrons?

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 = hν. B. The velocity of a photon is c. C. The momentum of a photon, p = hν/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:

The graph which shows the variation of (1/λ)² and the kinetic energy E of a free particle (where λ is the de Broglie wavelength of the particle) is:

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)

The de Broglie wavelength of an electron in the n = 2 state of the hydrogen atom is close to (Given Bohr radius a₀ = 0.052 nm):

Which of the following options represents the variation of photoelectric current with the property of light (intensity) shown on the x-axis?

A beam of light falls on a metal surface such that photo-electrons are generated. If the power of the light source starts to decrease linearly with time $t$, then the variation of the photocurrent $I$ and the magnitude of the stopping potential $|V|$ with time is best represented by:

A ray of light of wavelength $\lambda$ is incident on three photoelectric cells $1,2,3$ with threshold wavelengths $\lambda_1,\lambda_2,\lambda_3$ and stopping potentials $V_1,V_2,V_3$ respectively. Given $\lambda_1<\lambda,\ \lambda_2>\lambda,\ \lambda_3\gg\lambda$, the correct option is:

A photon and an electron, each of $20\,$eV energy, move in free space. The ratio of the linear momentum of the electron $p_e$ to that of the photon $p_{ph}$, $\dfrac{p_e}{p_{ph}}$, is: [speed of light $=3\times10^8\,\text{ms}^{-1}$, $e=1.6\times10^{-19}\,$C, $m_e=9\times10^{-31}\,$kg]

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 × 10⁻³⁴ J·s)

Match List I with List II. List-I: A. E = hν B. Diffraction and interference C. λ = h/p D. Compton effect List-II: I. de Broglie wavelength II. Particle nature of light III. Wave nature of light IV. Energy of photon Choose the correct answer from the options given below: