Dual Nature of Radiation

An electron (mass m) with initial velocity $\overrightarrow v = {v_0}\widehat i + {v_0}\widehat j$ is in an electric field $\overrightarrow E = - {E_0}\widehat k$. If $\lambda _0$ is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

The de-Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is :

An $\alpha$ particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are $\lambda$_$\alpha$ and $\lambda$_p respectively. The ratio ${{{{\lambda _p}} \over {{\lambda _\alpha }}}}$ is :

An electron of mass m_e and a proton of mass m_p = 1836 m_e are moving with the same speed. The ratio of their de Broglie wavelength ${{{}^\lambda electron} \over {{}^\lambda proton}}$ will be :

Given below are two statements : one is labeled as Assertion A and the other is labelled as Reason R. Assertion A : An electron microscope can achieve better resolving power than an optical microscope. Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below :

An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to that of photon is : (c being the velocity of light)

A particle is travelling 4 time 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 having de-Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is :