Dual Nature of Radiation

If the de Broglie wavelength of an electron is equal to the 10^–3 times the wavelength of a photon of frequency 6 $$\times$$ 10¹⁴ Hz, then the speed of electron is equal to : (Speed of light = 3 $$\times$$ 10⁸ m/s, Planck's constant = 6.63 $$\times$$ 10^–34 J.s, Mass of electron = 9.1 $$\times$$ 10^–31 kg)

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $${{{\lambda _A}} \over {{\lambda _B}}}$$ is close to :

Two particles move at right angle to each other. Their de-Broglie wavelengths are $$\lambda _1$$ and $$\lambda _2$$ respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength $$\lambda _2$$ of the final particle, is given by :

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '$$\lambda$$_x' and '$$\lambda$$_y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

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 :

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4.64 $$\times$$ 10^–26 kg, Boltzman constant: 1.38 $$\times$$ 10^–23 J/K, Planck constant : 6.63 $$\times$$ 10^–34 J.s)

An electron, a doubly ionized helium ion (He⁺⁺) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths $$\lambda$$_e, $$\lambda$$He⁺⁺ and $$\lambda$$_p is :

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 $$\times$$ 10^–4. The mass of the particle is close to

Particle A of mass m_A = $${m \over 2}$$ moving along the x-axis with velocity v₀ collides elastically with another particle B at rest having mass m_B = $${m \over 3}$$. If both particles move along the x-axis after the collision, the change $$\Delta$$$$\lambda$$ in de-Broglie wavlength of particle A, in terms of its de-Broglie wavelength ($$\lambda$$₀) before collision is :

A particle moving with kinetic energy E has de Broglie wavelength $$\lambda$$. If energy $$\Delta$$E is added to its energy, the wavelength become $$\lambda$$/2. Value of $$\Delta$$E, is :