When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $6.0 \mathrm{~V}$. This potential drops to $0.6 \mathrm{~V}$ if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the wavelength of the first source and the work function of the metal, respectively? [Take $\frac{h c}{e}=1.24 \times$ $10^{-6} \mathrm{JmC}^{-1}$.]

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u₁ and u₂, respectively. If the ratio u₁ : u₂ = 2 : 1 and hc = 1240 eV nm, the work function of the metal is nearly

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions $\phi_p=2.0~\mathrm{eV}$, $\phi_q=2.5~\mathrm{eV}$ and $\phi_r=3.0~\mathrm{eV}$, respecticely. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is (Take hc = 1240 eV nm)

The allowed energy for the particle for a particular value of $n$ is proportional to

If the mass of the particle is $m=1.0\times10^{-30}$ kg and $a=6.6$ nm, the energy of the particle in its ground state is closest to

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

Electrons with de-Broglie wavelength $\lambda$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 $\times$ 4 matrix given in the ORS.

Statement 1 :

If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change.

Statement 2 :

When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

The graph between $\frac{1}{\lambda}$ and stopping potential (V) of three metals having work functions $\phi_1, \phi_2$, and $\phi_3$ in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? (Here, $\lambda$ is the wavelength of the incident ray).

The potential energy of a particle of mass m is given by

$\mathrm{U}(x)=\left\{\begin{array}{cc}\mathrm{E}_{0} & 0 \leq x \leq 1 \\ 0 & x>1\end{array}\right.$

$\lambda_{1}$ and $\lambda_{2}$ are the de Broglie wavelengths of the particle, when $0 \leq x \leq 1$ and $x > 1$, respectively. If the total energy of particle is $2 \mathrm{E}_{0}$, find $\frac{\lambda_{1}}{\lambda_{2}}$.