Dual Nature of Radiation and Matter

When two monochromatic lights of frequency, $v$ $$ and $\frac{v}{2}$ $\frac{}{}$ are incident on a photoelectric metal, their stopping potential becomes $\frac{V_S}{2}$ $\frac{{}_{}}{}$ and $V_S$ ${}_{}$ respectively. The threshold frequency for this metal is

The speed of electrons in a scanning electron microscope is 1*10⁷ m/s. If protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of

A particle is traveling 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 :

Two identical photo-cathodes receive the light of frequencies f? and f? respectively. If the velocities of the photo-electrons coming out are v? and v? respectively, then

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)

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 * 10⁻²⁶ kg, Boltzman constant: 1.38 * 10⁻²³ J/K, Planck constant: 6.63 * 10⁻³⁴Js)

Particle A of mass mₐ = m/3 moving along the x-axis with velocity v₀ collides elastically with another particle B at rest having mass mₑ = m/3. If both particles move along the x axis after the collision, the change ∆λ in de-Broglie wavelength of particle A, in terms of its de-Broglie wavelength (λ₀) before collision is:

Given figure shows few data points in a photo electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surface is: (Plancks constant h = 6.62 * 10?³? J.s )

Particle $A$ $$ of mass $m_A=\frac{m}{2}$ ${}_{}\frac{}{}$ moving along the $x$ $$ -axis with velocity $v_0$ ${}_{}$ collides elastically with another particle $$ $B$ at rest having mass $m_B=\frac{m}{3}$ ${}_{}\frac{}{}$ . If both particles move along the $$ $x$ axis after the collision, the change $\mathrm{\Delta }\lambda$ $$ in de-Broglie wavelength of particle $A$ $$ , in terms of its de-Broglie wavelength $\left({}_{}\right)$ $\left({\lambda }_0\right)$ before collision is:

Two sources of light emit $X$  - rays of wavelength   $1\mathrm{n}\mathrm{m}$ and visible light of wavelength $500\mathrm{n}\mathrm{m}$   , respectively. Both the sources emit light of the same power $200\mathrm{W}$   . The ratio of the number density of photons of $X$  - rays to the number density of photons of the visible light of the given wavelengths is: