Dual Nature of Radiation and Matter

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

An α a particle and a proton are accelerated from rest by a potential difference of 220V. After this, their de Broglie wavelengths are  ${\lambda }_{\alpha }and{\lambda }_P$ respectively. The ratio $\frac{{\lambda }_P}{{\lambda }_{\alpha }}is:$

The wavelength of an X-ray beam is $10\stackrel{o}{A}.$ The mass of a fictitious particle having the same energy as that of the X-ray photons is $\frac{x}{3}hkg.$ The value of x is………. (h = Planck's constant)

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 $\frac{{\lambda }_{electron}}{{\lambda }_{proton}}$  will be

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43V. The new wavelength is

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  $E=hv$ .

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 charge.

Choose the correct answer from the options given below:

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are $8*10^8 N m^{-2}$ and $2*10^{11} N m^{-2}$ , is:

A parallel beam of light of wavelength 900nm and intensity 100Wm^-2 is incident on a surface perpendicular to the beam. The number of photons crossing 1cm² area perpendicular to the beam in one second is

The graph which shows the variation of $\left(\frac{1}{{\lambda }^2}\right)$ and its kinetic energy, $E$ is (where $\lambda$ is de Broglie wavelength of a free particle):