The electric field at a point associated with a light wave
Question: The electric field at a point associated with a light wave isE $=\left(100 \mathrm{Vm}^{-1}\right) \sin \left[\left(3.0 \times 10^{15} \mathrm{~s}^{-1}\right) \mathrm{t}\right] \sin \left[\left(6.0 \times 10^{15} \mathrm{~s}^{-1}\right) \mathrm{t}\right]$. If this light falls on a metal surface with a work function of $2.0 \mathrm{eV}$, what will be the maximum kinetic energy of the photoelectrons? Solution:...
Read More →The electric field associated with a light wave is given
Question: The electric field associated with a light wave is given byE $=E_{0} \sin \left(1.57 \times 10^{7} \mathrm{~m}^{-1}\right)(x-c t)$. Find the stopping potential when this light is used in an experiment on photoelectric effect with the emitter having work function $1.9 \mathrm{eV}$. Solution:...
Read More →The electric field associated with a monochromatic beam is
Question: The electric field associated with a monochromatic beam is $1.2 \times 10^{15}$ times per second. Find the maximum kinetic energy of the photoelectrons when this light falls on a metal surface whose work function is $2.0 \mathrm{eV}$. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If the function $f(x)=\left\{\begin{array}{c}\frac{1-\cos 4 x}{8 x^{2}}, x \neq 0 \\ k, x=0\end{array}\right.$ is continuous at $x=0$ and then $k=?$ A. 1 B. 2 C. $\frac{1}{2}$ D. $\frac{-1}{2}$ Solution:...
Read More →In an experiment on photoelectric effect,
Question: In an experiment on photoelectric effect, the stopping potential is measured for monochromatic light beams corresponding to different wavelengths. The data collected are as follows: Plot the stopping potential against inverse of wavelength $(1 / \lambda)$ on a graph paper and find (a) Planck's constant (b) The work function of the emitter and (c) The threshold wavelength. Solution:...
Read More →When a metal plate is exposed to a monochromatic beam of light of wavelength
Question: When a metal plate is exposed to a monochromatic beam of light of wavelength $400 \mathrm{~nm}$, a negative potential of $1.1 \mathrm{~V}$ is needed to stop the photo current. Find the threshold wavelength for the metal. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $f(x)=\left\{\begin{array}{c}\mathrm{kx}+5, \text { when } \mathrm{x} \leq 2 \\ \mathrm{x}+1, \text { when } \mathrm{x}2\end{array}\right.$ is continuous at $\mathrm{x}=2$ then $\mathrm{k}=?$ A. 2 B. $-2$ C. 3 D. $-3$ Solution:...
Read More →Find the maximum magnitude of the linear momentum of
Question: Find the maximum magnitude of the linear momentum of a photoelectron emitted when a wavelength of $400 \mathrm{~nm}$ falls on a metal with work function $2.5 \mathrm{eV}$. Solution:...
Read More →The work function of a photoelectric material is 4.0 eV.
Question: The work function of a photoelectric material is $4.0 \mathrm{eV}$. (a) What is the threshold wavelength? (b) Find the wavelength of light for which the stopping potential is $2.5 \mathrm{~V}$. Solution:...
Read More →The work function of a metal is
Question: The work function of a metal is $2.5 \times 10^{-19} \mathrm{~J}$. (a) Find the threshold frequency for photoelectric emission. (b) If the metal is exposed to a light beam of frequency $6.0 \times 10^{14} \mathrm{~Hz}$, what will be the stopping potential? Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: The function $f(x)=\left\{\begin{array}{ll}1+x, \text { when } x \leq 2 \\ 5-x, \text { when } x2\end{array}\right.$ is A. continuous as well as differentiable at $x=2$ B. continuous but not differentiable at $x=2$ C. differentiable but not continuous at $x=2$ D. none of these Solution:...
Read More →Find the maximum kinetic energy of the photoelectrons ejected
Question: Find the maximum kinetic energy of the photoelectrons ejected when light of wavelength $350 \mathrm{~nm}$ is incident on a cesium surface. Work function of cesium $=1.9 \mathrm{eV}$ Solution:...
Read More →Two neutral particles are kept 1 m apart.
Question: Two neutral particles are kept $1 \mathrm{~m}$ apart. Suppose by some mechanism some charge is transferred from one particle to the other and the electric potential energy lost is completely converted into a photon. Calculate the longest and the next smaller wavelength of the photon possible. Solution:...
Read More →Show that it is not possible for a photon to be completely absorbed by a free electron.
Question: Show that it is not possible for a photon to be completely absorbed by a free electron. Solution:...
Read More →Consider the situation described in the previous problem.
Question: Consider the situation described in the previous problem. Show that the force on the sphere due to the light falling on it is the same even if the sphere is not perfectly absorbing. Solution: Consider az sphere of centre $\mathrm{O}$ and radius OP. As shown in the figure, the radius OP of the sphere is making an angle $\theta$ with $\mathrm{OZ}$. Let us rotate the radius about $\mathrm{OZ}$ to get another circle on the sphere. The part of the sphere between the circle is a ring of area...
Read More →A sphere of radius 1.00 cm is placed in the path of a parallel beam of
Question: A sphere of radius $1.00 \mathrm{~cm}$ is placed in the path of a parallel beam of light of large aperture. The intensity of the light is $0.5 \mathrm{~W}$ $\mathrm{cm}^{-2}$. If the sphere completely absorbs the radiation falling on it, find the force exerted by the light beam on the sphere. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: The function $f(\mathrm{x})=|\mathrm{x}| \forall \mathrm{x} \in \mathrm{R}$ is A. continuous but not differentiable at $x=0$ B. differentiable but not continuous at $x=0$ C. neither continuous nor differentiable at $x=0$ D. none of these Solution:...
Read More →A 100 W light bulb is placed at the centre of a spherical chamber of radius 20 cm.
Question: A $100 \mathrm{~W}$ light bulb is placed at the centre of a spherical chamber of radius $20 \mathrm{~cm}$. Assume that $60 \%$ of the energy supplied to the bulb is converted into light and that the surface of the chamber is perfectly absorbing. Find the pressure exerted by the light on the surface of the chamber. Solution:...
Read More →A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light,
Question: A totally reflecting, small plane mirror placed horizontally faces a parallel beam of light, as shown in the figure. The mass of the mirror is $20 \mathrm{~g}$. Assume that there is no absorption in the lens and that $30 \%$ of the light emitted by the source goes through the lens. Find the power of the source needed to support the weight of the mirror. Figure 42-E1 Solution:...
Read More →A beam of white light is incident normally on a plane surface absorbing
Question: A beam of white light is incident normally on a plane surface absorbing $70 \%$ of the light and reflecting the rest. If the incident beam carries $10 \mathrm{~W}$ of power. find the force exerted bv it on the surface. Solution:...
Read More →A parallel beam of monochromatic light of wavelength
Question: A parallel beam of monochromatic light of wavelength $663 \mathrm{~nm}$ is incident on a totally reflecting plane mirror. The angle of incidence is $60^{\circ}$ and the number of photons striking the mirror per second is $1.0 \times 10^{19}$. Calculate the force exerted by the light beam on the mirror. Solution:...
Read More →When the sun is directly overhead,
Question: When the sun is directly overhead, the surface of the earth receives $1.4 \times 10^{3} \mathrm{~W} \mathrm{~m}^{-2}$ of sunlight. Assume that the light is monochromatic with average wavelength $500 \mathrm{~nm}$ and that no light is absorbed in between the sun and the earth's surface. The distance between the sun and the earth is $1.5 \times 10^{11} \mathrm{~m}$. (a) Calculate the number of photons falling per second on each square metre of earth's surface directly below the sun. (b) ...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: Let $f(\mathrm{x})=\mathrm{x}^{3 / 2}$. Then, $f^{\prime}(0)=$ ? A. $\frac{3}{2}$ B. $\frac{1}{2}$ C. does not exist D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: The value of $k$ for which $f(x)=\left\{\begin{array}{c}\frac{3 x+4 \tan x}{2}, \text { when } x \neq 0 \\ k, \text { when } x=0\end{array}\right.$ is continuous at $x=0$, is A. 7 B. 4 C. 3 D. none of these Solution: $\therefore K=7 .$...
Read More →Calculate the number of photons emitted per second by
Question: Calculate the number of photons emitted per second by a $10 \mathrm{~W}$ sodium vapour lamp. Assume that $60 \%$ of the consumed energy is converted into light. Wavelength of sodium light $=590 \mathrm{~nm}$ Solution:...
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