Calculate the smallest wavelength of radiation that may be emitted by hydrogen
Question: Calculate the smallest wavelength of radiation that may be emitted by hydrogen $\mathrm{He}^{+}$and $\mathrm{Li}^{++}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The function $f(\mathrm{x})=\mathrm{x}^{3}-27 \mathrm{x}+8$ is increasing when A. $|\mathrm{x}|3$ B. $|\mathrm{x}|3$ C. $-3x3$ D. none of these Solution:...
Read More →Find the wavelength of the radiation emitted by hydrogen in the transitions
Question: Find the wavelength of the radiation emitted by hydrogen in the transitions (a) $n=3$ to $n=2$, (b) $n=5$ to $n=4$, (c) $n=10$ to $n=9$. Solution:...
Read More →The Bohr radius is given by
Question: The Bohr radius is given by $\alpha_{0}=\frac{\varepsilon_{0} \mathrm{~h}_{2}}{\mathrm{mks}^{2}}$ Verify that the RHS has dimensions of length. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The function $f(x)=x^{3}+6 x^{2}+9 x+3$ is decreasing for A. $1x3$ B. $x1$ C. $x1$ D. $x1$ or $x3$ Solution: But for $-1x-3$ it is decreasing....
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The function $f(x)=3 x+\cos 3 x$ is A. increasing on $R$ B. decreasing on $\mathrm{R}$ C. strictly increasing on $R$ D. strictly decreasing on $R$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The function $f(x)=4-3 x+3 x^{2}-x^{3}$ is A. decreasing on $\mathrm{R}$ B. increasing on $\mathrm{R}$ C. strictly decreasing on $R$ D. strictly increasing on $R$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The function $f(x)=x^{3}+6 x^{2}+15 x-12$ is A. strictly decreasing on $R$ B. strictly increasing on R C. increasing in $(-\infty, 2)$ and decreasing in $(2, \infty)$ D. none of these Solution:...
Read More →A light beam of wavelength 400 nm is incident on a metal plate of work function 2.2 eV.
Question: A light beam of wavelength $400 \mathrm{~nm}$ is incident on a metal plate of work function $2.2 \mathrm{eV}$. (a) A particular electron absorbs a photon and makes two collisions before coming out of the metal. Assuming that $10 \%$ of the extra energy is lost to the metal in each collision, find the kinetic energy of this electron as it comes out of the metal. (b) Under the same assumptions, find the maximum number of collisions the electron can suffer before it becomes unable to come...
Read More →A small metal plate (work function φ) is kept at a distance d from
Question: A small metal plate (work function $\varphi$ ) is kept at a distance $d$ from a singly-ionised, fixed ion. A monochromatic light beam is incident on the metal plate and photoelectrons are emitted. Find the maximum wavelength of the light beam, so that some of the photoelectrons may go round the ion along a circle. Solution:...
Read More →A horizontal cesium plate (φ = 1.9 eV) is moved vertically downward
Question: A horizontal cesium plate $(\varphi=1.9 \mathrm{eV})$ is moved vertically downward at a constant speed $v$ in a room full of radiation of wavelength $250 \mathrm{~nm}$ and above. What should be the minimum value of $v$ so that the vertically-upward component of velocity is non-positive for each photoelectron? Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: Let $f(x)=\left\{\begin{array}{r}\frac{x^{2}-2 x-3}{x+1^{2}}, \text { when } x \neq-1 \\ k, \text { when } x=-1\end{array}\right.$ If $f(\mathrm{x})$ is continuous at $\mathrm{x}=-1$ then $\mathrm{k}=?$ A. 4 B. $-4$ C. $-3$ D. 2 Solution:...
Read More →Consider the situation of the previous problem.
Question: Consider the situation of the previous problem. Consider the faster electron emitted parallel to the large metal plate. Find the displacement of this electron parallel to its initial velocity before it strikes the large metal plate. Solution:...
Read More →A small piece of cesium metal (φ = 1.9 eV) is kept at a distance of 20 cm
Question: A small piece of cesium metal ( $\varphi=1.9 \mathrm{eV})$ is kept at a distance of $20 \mathrm{~cm}$ from a large metal plate with a charge density of $1.0 \times 10^{-9} \mathrm{C} \mathrm{m}^{-2}$ on the surface facing the cesium piece. A monochromatic light of wavelength $400 \mathrm{~nm}$ is incident on the cesium piece. Find the minimum and maximum kinetic energy of the photoelectrons reaching the large metal plate. Neglect any change in electric field due to the small piece of c...
Read More →In a photoelectric experiment,
Question: In a photoelectric experiment, the collector plate is at $2.0 \mathrm{~V}$ with respect to the emitter plate made of copper $(\varphi=4.5 \mathrm{eV})$. The emitter is illuminated by a source of monochromatic light of wavelength $200 \mathrm{~nm}$. Find the minimum and maximum kinetic energy of the photoelectrons reaching the collector. Solution:...
Read More →In the arrangement shown in the figure,
Question: In the arrangement shown in the figure, $y=1.0 \mathrm{~mm}, d=0.24 \mathrm{~mm}$ and $D=1.2 \mathrm{~m}$. The work function of the material of the emitter is $2.2 \mathrm{eV}$. Find the stopping potential $V$ needed to stop the photocurrent. Figure 42-E4 Solution:...
Read More →In an experiment on photoelectric effect,
Question: In an experiment on photoelectric effect, the emitter and the collector plates are placed at a separation of $10 \mathrm{~cm}$ and are connected through an ammeter without any cell. A magnetic field $B$ exists parallel to the plates. The work function of the emitter is $2.39 \mathrm{eV}$ and the light incident on it has wavelengths between $400 \mathrm{~nm}$ and $600 \mathrm{~nm}$. Find the minimum value of B for which the current registered by the ammeter is zero. Neglect any effect o...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: At $\mathrm{x}=2, \quad f(\mathrm{x})=|\mathrm{x}|$ is A. continuous but not differentiable B. differentiable but not continuous C. continuous as well as differentiable D. none of these Solution:...
Read More →A silver ball of radius 4.8 cm is suspended by a thread in a vacuum chamber.
Question: A silver ball of radius $4.8 \mathrm{~cm}$ is suspended by a thread in a vacuum chamber. Ultraviolet light of wavelength 200 nm is incident on the ball for some time during which light energy of $1.0 \times 10^{-7} \mathrm{~J}$ falls on the surface. Assuming that on average, one photon out of every ten thousand is able to eject a photoelectron, find the electric potential at the surface of the ball, assuming zero potential at infinity. What is the potential at the centre of the ball? S...
Read More →In an experiment on photoelectric effect, light of wavelength
Question: In an experiment on photoelectric effect, light of wavelength $400 \mathrm{~nm}$ is incident on a cesium plate at the rate of $5.0 \mathrm{~W}$. The potential of the collector plate is made sufficiently positive with respect to the emitter, so that the current reaches its saturation value. Assuming that on average, one out of every $10^{6}$ photons is able to eject a photoelectron, find the photocurrent in the circuit. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If the function $f(x)=\left\{\begin{array}{c}\frac{k \cos x}{(\pi-2 x)}, \text { when } x \neq \frac{\pi}{2} \\ 3, \text { when } x=\frac{\pi}{2}\end{array}\right.$ be continuous at $x=\frac{\pi}{2}$, then the value of $k$ is A. 3 B. $-3$ C. $-5$ D. 6 Solution:...
Read More →A photographic film is coated with a silver bromide layer.
Question: A photographic film is coated with a silver bromide layer. When light falls on this film, silver bromide molecules dissociate and the film records the light there. A minimum of $0.6 \mathrm{eV}$ is needed to dissociate a silver bromide molecule. Find the maximum wavelength of light that can be recorded by the film. Solution:...
Read More →The figure is the plot of stopping potential versus the frequency of
Question: The figure is the plot of stopping potential versus the frequency of the light used in an experiment on photoelectric effect. Find (a) The ratio $h / e$ and (b) The work function. Figure 42-E2 Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If the function $f(x)=\left\{\begin{array}{c}\frac{\sin ^{2} a x}{x^{2}}, \text { when } x \neq 0 \\ k, \text { when } x=0\end{array}\right.$ is continuous at $x=0$ then $k=?$ A. a B. $\mathrm{a}^{2}$ C. $-2$ D. $-4$ Solution:...
Read More →A monochromatic light source of intensity
Question: A monochromatic light source of intensity $5 \mathrm{~mW}$ emits $8 \times 10^{15}$ photons per second. This light ejects photoelectrons from a metal surface. The stopping potential for this setup is $2.0 \mathrm{~V}$. Calculate the work function of the metal. Solution:...
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