Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in the following: $f(\mathrm{x})=|\mathrm{x}|$ has A. minimum at $x=0$ B. maximum $x=0$ C. neither a maximum nor a minimum at $x=0$ D. none $f$ these Solution:...
Read More →Radiation from hydrogen discharge tube falls on a cesium plate.
Question: Radiation from hydrogen discharge tube falls on a cesium plate. Find the maximum possible kinetic energy of the photoelectrons. Work function of cesium is $1.9 \mathrm{eV}$. Solution:...
Read More →Light from Balmer series of hydrogen is able to eject photoelectrons from a metal.
Question: Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be the maximum work function of the metal? Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The least value of $k$ for which $f(x)=x^{2}+k x+1$ is increasing on $(1,2)$, is A. $-2$ B. -1 C. 1 D. 2 Solution:...
Read More →The light emitted in the transition n=3 to n=2 in hydrogen is called Ha light.
Question: The light emitted in the transition $\mathrm{n}=3$ to $\mathrm{n}=2$ in hydrogen is called $\mathrm{H}_{\mathrm{a}}$ light. Find the maximum work function a metal can have so that $\mathrm{H}_{\mathrm{a}}$ light can emit photoelectrons from it. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $f(x)=\frac{x}{\left(x^{2}-1\right)}$ is increasing in A. $(-1,1)$ B. $(-1, \infty)$ C. $(-\infty,-1) \cup(1, \infty)$ D. none of these Solution:...
Read More →When a photon is emitted from an atom,
Question: When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from $n=3$ to $n=2$ Calculate the fractional change in the wavelength of light emitted, due to the recoil. Solution:...
Read More →When a photon is emitted by a hydrogen atom,
Question: When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. Calculate the momentum carried by the photon when a hydrogen atom emits light of wavelength $656.3 \mathrm{~nm}$. With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom $=1.67 \times 10^{-27} \mathrm{~kg}$. Find the kinetic energy of recoil of the atom. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: If $f(\mathrm{x})=\mathrm{kx}^{3}-9 \mathrm{x}^{2}+9 \mathrm{x}+3$ is increasing for every real number $\mathrm{x}$, then A. $k3$ B. $k \geq 3$ C. $k3$ D. $k \leq 3$ Solution:...
Read More →A neutron moving with a speed v strikes a hydrogen atom in ground
Question: A neutron moving with a speed v strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron mass of hydrogen $=1.67 \times 10^{-27} \mathrm{~kg}$. Solution:...
Read More →A hydrogen atom moving at speed v collides with another hydrogen
Question: A hydrogen atom moving at speed $v$ collides with another hydrogen atom kept at rest. Find the minimum value of $v$ for which one of the atoms may get ionized. The mass of a hydrogen atom $=1.67 \times 10^{-27} \mathrm{~kg}$. Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $f(\mathrm{x})=[\mathrm{x}(\mathrm{x}-3)]^{2}$ is increasing in A. $(0, \infty)$ B. $(-\infty, 0)$ C. $(1,3)$ D. $\left(0, \frac{3}{2}\right) \cup(3, \infty)$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $f(x)=(x+1)^{3}(x-3)^{3}$ is increasing in A. $(-\infty, 1)$ B. $(-1,3)$ C. $(3, \infty)$ D. $(1, \infty)$ Solution:...
Read More →A neutron having kinetic energy 12.5 eV collides with
Question: A neutron having kinetic energy $12.5 \mathrm{eV}$ collides with a hydrogen atom at rest. Neglect the difference in mass between the neutron and the hydrogen atom and assumes that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event. Solution: In elastic collision between two bodies of equal masses, the velocity gets interchange. Since the hydrogen atom is at rest, after collision, the velocity of the neutron will be zero....
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $f(\mathrm{x})=\sin \mathrm{x}-\mathrm{kx}$ is decreasing for all $\mathrm{x} \notin \mathrm{R}$, when A. $k1$ B. $k \leq 1$ C. $k1$ D. $\mathrm{k} \leq 1$ Solution:...
Read More →Electrons are emitted from an electron gun at almost zero velocity and
Question: Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field $E$ through a distance of $1.0 \mathrm{~m}$. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength $656.3 \mathrm{~nm}$ may be emitted by the hydrogen? Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $f(\mathrm{x})=\mathrm{x}^{2} \mathrm{e}^{-\mathrm{x}}$ is increasing in A. $(-2,0)$ B. $(0,2)$ C. $(2, \infty)$ D. $(-\infty, \infty)$ Solution: But in the interval $(0,2)$ the function is increasing....
Read More →A beam of monochromatic light of wavelength λ ejects photoelectrons
Question: A beam of monochromatic light of wavelength $\lambda$ ejects photoelectrons from a cesium surface $(\phi=1.9$ eV). These photoelectrons are made to collide with hydrogen atoms in ground state. Find the maximum value of $\lambda$ for which Hydrogen atoms may be ionized, Hydrogen atoms may get excited from the ground state to the first excited state and The excited hydrogen atoms may emit visible light. Solution:...
Read More →A parallel beam of light of wavelength 100 nm passes through a sample of
Question: A parallel beam of light of wavelength $100 \mathrm{~nm}$ passes through a sample of atomic hydrogen gas in ground state. a. Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon moving in the same direction as the incident photo. Neglecting the light emitted by the excited hydrogen atoms in the direction of the incident beam, what wavelength may be observed in the transmitted beam? b. A radiation detector is placed n...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $f(\mathrm{x})=\mathrm{x}^{\mathrm{x}}$ is decreasing in the interval A. $(0, \mathrm{e})$ B. $\left(0, \frac{1}{\mathrm{e}}\right)$ C. $(0,1)$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: $f(x)=\frac{x}{\sin x}$ is A. increasing in $(0,1)$ B. decreasing in $(0,1)$ C. increasing in $\left(0, \frac{1}{2}\right)$ and decreasing in $\left(\frac{1}{2}, 1\right)$ D. none of these Solution: $\therefore f(x)$ is increasing in $(0,1)$...
Read More →A hydrogen atom in ground state absorbs a photon of ultraviolet radiation
Question: A hydrogen atom in ground state absorbs a photon of ultraviolet radiation of wavelength $50 \mathrm{~nm}$. Assuming that the entire photon energy is taken up by the electron, with what kinetic energy will the electron be ejected? Solution:...
Read More →Radiation coming from transition n=2 to n=1
Question: Radiation coming from transition $n=2$ to $n=1$ of hydrogen atoms falls on helium ions in $n=1$ and $n=2$ states. What are the possible transitions of helium, ions as they absorb energy from the radiation? Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: $f(x)=(\sin x-\cos x)$ is decreasing in A. $\left(0, \frac{3 \pi}{4}\right)$ B. $\left(\frac{3 \pi}{4}, \frac{7 \pi}{4}\right)$ C. $\left(\frac{7 \pi}{4}, 2 \pi\right)$ D. none of these Solution: Given:...
Read More →A beam of light having wavelength distributed uniformly between
Question: A beam of light having wavelength distributed uniformly between $450 \mathrm{~nm}$ to $550 \mathrm{~nm}$ passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam? Solution:...
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