Dual Nature Of Radiation - Modern Physics - Physics Previous Year Questions

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 \(\frac{\lambda_{1}}{\lambda_{2}}\).

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).

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.

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.

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

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

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

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)

An \(\alpha\)-particle and a proton are accelerated from the rest by a potential difference of 100 V. After this, their de Broglie wavelengths are \(\lambda\)_\(\alpha\) and \(\lambda\)_p, respectively. The ratio \({{{\lambda _p}} \over {{\lambda _\alpha }}}\), to the nearest integer, is _____________.

The activity of a freshly prepared radioactive sample is 10¹⁰ disintegrations per second, whose mean life is 10⁹ s. The mass of an atom of this radioisotope is 10^\(-\)25 kg. The mass (in mg) of the radioactive sample is _________.

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the spheres is A \(\times\) 10^Z (where 1 < A < 10). The value of Z is _____________.

A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is ____________. (Take the proton mass, \({m_p} = (5 \times 3) \times {10^{ - 27}}\) kg; \(h/e = 4.2 \times {10^{ - 15}}\) J.s/C; \({1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}\) m/F; 1 fm = 10¹⁵ m.)

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is ___________.

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