Embibe Experts Solutions for Chapter: Dual Nature of Matter and Radiation, Exercise 1: TS EAMCET - 5 August 2021 Shift 1

A photodiode sensor is used to measure the output of a $300 \mathrm{W}$ lamp kept $10 \mathrm{m}$ away The sensor has an opening of $2 \mathrm{cm}$ in diameter. How many photons enter the sensor if the wavelength of the light is $660 \mathrm{nm}$ and the exposure time is $100 \mathrm{m} \mathrm{s}$. (Assume that all the energy of the lamp is given off as light and $\mathrm{h}=6.6\times {10}^{-34} \mathrm{J} \mathrm{s}$ )

To excite the spectral line of wavelength $4960 \stackrel{\circ }{\mathrm{A}}$ of an atom, an excitation energy of $7.7 \mathrm{eV}$ is required. The ground state energy of the atom is $10.5 \mathrm{eV}$. The energies of two levels involved in the emission of $4960 \stackrel{\circ }{\mathrm{A}}$ line are (Assume, $hc=1240 \mathrm{eV} \mathrm{nm}$, where $h$ is Planck's constant and $\mathrm{c}$ is speed of light)

A beam of photons with an energy of $10.5 \mathrm{eV}$ strike a metal plate. The photoelectrons are emitted with maximum velocity of $1.6\times {10}^6 \mathrm{m} {\mathrm{s}}^{-1}$. The work function of the metal is
(Assume mass of electron $=9\times {10}^{-31} \mathrm{kg}$ and Charge of electron $=1.6\times {10}^{-19}\mathrm{C}$)

At an incident radiation frequency of $v_1$, which is greater than the threshold frequency, the stopping potential for a certain metal is $V_1$. At frequency $2v_1$ the stopping potential is $3V_1$. If the stopping potential at frequency $4v_1$ is $n{V}_1$, then $n$ is

The work function of a metal is $h{v}_0$. Light of frequency $v$ falls on this metal. The photoelectric effect will take place only if

The de Broglie wavelength of an electron of kinetic energy $9 \mathrm{eV}$ is (take $h=4\times {10}^{-15} \mathrm{eV}.\sec$, $c=3\times {10}^{10} \mathrm{cm} {\sec }^{-1}$ and the mass $m_e$ of electron as $m_e{c}^2=0.5 \mathrm{MeV}$)

Which of the following particle has the shortest de-Broglie wavelength?

The de-Broglie wavelength of an electron having kinetic energy $100 \mathrm{eV}$ is,
[Use $h=4.14\times {10}^{-15} \mathrm{eVs},$ mass of electron $=\frac{0.5\times {10}^6}{c^2}\mathrm{eV}, 1\mathrm{pm}={10}^{-12} \mathrm{m}$]