Chapter 25

If \(\alpha\)-particle and proton are accelerated through the same potential difference, then the ratio of de-Broglie wavelength of \(\alpha\)-particle and proton is (a) \(\sqrt{2}\) (b) \(2 \sqrt{2}\) (c) \(\frac{1}{2 \sqrt{2}}\) (d) \(\frac{1}{\sqrt{2}}\)

Assertion Work function of copper is greater than the work function of sodium, but both have same value of threshold frequency and threshold wavelength. Reason The frequency is inversely proportional to wavelength.

When a point source of light is \(1 \mathrm{~m}\) away from a photoelectric cell, the photoelectric current is found to be \(I \mathrm{~mA}\). If the same source is placed at \(4 \mathrm{~m}\) from the same photoelectric cells, the photoelectric current (in \(\mathrm{mA}\) ) will be (a) \(\frac{1}{16}\) (b) \(\frac{I}{4}\) (c) \(4 I\) (d) \(16 I\)

Assertion Stopping potential is a measure of \(\mathrm{KE}\) of photoelectron. Reason \(W=e V_{s}=\frac{1}{2} m v^{2}=\mathrm{KE}\)

The work function of tungsten and sodium are \(4.5 \mathrm{eV}\) and \(2.3 \mathrm{eV}\) respectively. If the threshold wavelength, \(\lambda\) for sodium is \(5460 \AA\), the value of \(\lambda\) for tungsten is (a) \(2791 \dot{\mathrm{A}}\) (b) \(3260 \dot{A}\) (c) \(1925 \mathrm{~A}\) (d) \(1000 \mathrm{~A}\)

Assertion A photon has no rest mass, yet it carries definite momentum. Reason Momentum of photon is due to energy hence its equivalent mass.

A photon of energy \(E\) ejects a photoelectrons from a metal surface whose work function is \(W_{0}\). If this electron enters into a uniform magnetic field of induction \(B\) in a direction perpendicular to the field and describes a circular path of radius \(r\), then the radius, \(r\) is given by (a) \(\sqrt{\frac{2 m\left(W_{0}-E\right)}{e B}}\) (b) \(\sqrt{\frac{2 e\left(E-W_{0}\right)}{m B}}\) (c) \(\sqrt{\frac{2 m\left(E-W_{0}\right)}{e B}}\) (d) \(\sqrt{\frac{2 m W_{0}}{e B}}\)

The energy flux of sunlight reaching the surface of the earth is \(1.388 \times 10^{3} \mathrm{~W} / \mathrm{m}^{2}\). How many photons (nearly) per square metre are incident on the earth per second? Assume that the photons in the sunlight have an average wavelength of \(550 \mathrm{~nm} .\) [NCERT] (a) \(3.8 \times 10^{21}\) photon \(/ \mathrm{m}^{2}-\mathrm{s} \quad\) (b) \(4.1 \times 10^{18}\) photon \(/ \mathrm{m}^{2}-5\) (c) \(2.6 \times 10^{19}\) photon \(/ \mathrm{m}^{2}-\mathrm{s}\) (d) \(1.9 \times 10^{20}\) photon \(/ \mathrm{m}^{2}-\mathrm{s}\)

The work function for the surface of \(\mathrm{Al}\) is \(4.2 \mathrm{eV}\). How much potential difference will be required to just stop the emission of maximum energy electrons emitted by light of \(2000 \AA\) A ? (a) \(1.51 \mathrm{~V}\) (b) \(1.99 \mathrm{~V}\) (c) \(2.99 \mathrm{~V}\) (d) None of these

Light of wavelength \(\lambda\) falls on a metal having work function \(\frac{h c}{\lambda_{0}} .\) Photoelectric effect will take place only if [DCE 2009] (a) \(\lambda \geq \lambda_{0}\) (b) \(\lambda \geq 2 \lambda_{0}\) (c) \(\lambda \leq \lambda_{0}\) (d) \(\lambda=4 \lambda_{0}\)

Two monochromatic beams \(A\) and \(B\) of equal intensity \(I\), hit a screen. The number of photons hitting the screen by beam \(A\) is twice that by beam \(B\). Then, what inference can you move about their frequencies? (a) The frequency of beam \(B\) is twice that of \(A\) (b) The frequency of beam \(B\) is half that of \(A\) (c) The frequency of beam \(A\) is twice of \(B\) (d) None of the above

A neutrons beam of energy \(E\) scatters from atoms on a surface with a spacing \(d=0.1 \mathrm{~nm}\). The first maximum of intensity in the reflected beam occurs at \(\theta=30^{\circ}\). The kinetic energy \(E\) of the beam (in \(\mathrm{eV}\) ) is \(\begin{array}{ll}\text { (a) } 10.2 \mathrm{eV} & \text { (b) } 5.02 \mathrm{eV}\end{array}\) (c) \(0.21 \mathrm{eV}\) (d) \(0.78 \mathrm{eV}\)

Which phenomenon best supports the theory that matter has a wave nature ? (a) Electron momentum (b) Electron diffraction (c) Photon momentum (d) Photon diffraction

Light of wavelength \(\lambda\) strikes a photo sensitive surface and electrons are ejected with kinetic energy \(E\). If the \(\mathrm{KE}\) is to be increased to \(2 E\), the wavelength must be changed to \(\lambda^{\prime}\) where (a) \(\lambda^{\prime}=\frac{\lambda}{2}\) (b) \(\lambda^{\prime}=2 \lambda\) (c) \(\frac{\lambda}{2}<\lambda^{\prime}<\lambda\) (d) \(\lambda^{\prime}>\lambda\)

Out of a photon and an electron the equation \(E=p c\), is valid for \(\quad\) [BVP Engg. 2008] (a) both (b) neither (c) photon only (d) electron only

The threshold wavelength for a metal having work function \(W_{0}\) is \(\lambda_{0}\). What is the threshold wavelength for a metal whose work function is \(\frac{W_{0}}{2} ?\) (a) \(4 \lambda_{0}\) (b) \(2 \lambda_{0}\) (c) \(\frac{\lambda_{0}}{2}\) (d) \(\frac{\lambda_{0}}{4}\)

The work function of a substance is \(4.0 \mathrm{eV}\). The longest wavelength of light that can cause photoelectric emission from this substance approximately. (a) \(540 \mathrm{~nm}\) (b) \(400 \mathrm{~nm}\) (c) \(310 \mathrm{~nm}\) (d) \(220 \mathrm{~nm}\)

An electron and photon have same wavelength. If \(E\) is the energy of photon and \(p\) is the momentum of electron, then the magnitude of \(\frac{E}{p}\) in SI unit is (a) \(3.33 \times 10^{-9}\) (b) \(3.0 \times 10^{8}\) (c) \(1.1 \times 10^{-19}\) (d) \(9 \times 10^{16}\)

The wavelength of de-Broglie wave associated with a thermal neutron of mass \(m\) at absolute temperature \(T\) is given by (Here, \(k\) is the Boltzmann constant) (a) \(\frac{h}{\sqrt{2 m k T}}\) (b) \(\frac{h}{\sqrt{m k T}}\) (c) \(\frac{h}{\sqrt{3 k m T}}\) (d) \(\frac{h}{2 \sqrt{m k T}}\)

Photon of frequency \(v\) has a momentum associated with it. If \(c\) is the velocity of the light, the moments is (a) \(\frac{v}{c}\) (b) \(h v c\) (c) \(\frac{h v}{c^{2}}\) (d) \(\frac{h v}{c}\)

An electron is moving with an initial velocity \(\mathbf{v}=v_{0} \hat{\mathbf{i}}\) and is in a magnetic field \(\mathbf{B}=B_{0} \hat{\mathbf{j}}\).Then it's de-Broglie wavelength \(\quad\) (a) remains constant (b) increases with time (c) decreases with time (d) increases and decreases periodically

An electron (mass \(m\) ) with an initial velocity \(\mathbf{v}=v_{0} \hat{\mathbf{i}}\left(\mathbf{v}_{0}>0\right)\) is in an electric field \(\mathbf{E}=E_{0} \hat{\mathbf{i}}\left(E_{0}=\right.\) constant \(\left.>0\right)\) field. It's de-Broglie wavelength at time \(t\) is given by (a) \(\frac{\lambda_{0}}{\left(1+\frac{e E_{0}}{m} \frac{t}{v_{0}}\right)}\) (b) \(\lambda_{0}\left(1+\frac{e E_{0} t}{m v_{0}}\right)\) (c) \(\lambda_{0}\) (d) \(\lambda_{0} t\)

If the mass of neutral \(=1.7 \times 10^{-27} \mathrm{~kg}\), then the de- Broglie wavelength of neutral of energy \(3 \mathrm{eV}\) is \(\left(h=6.6 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right)\) (a) \(1.6 \times 10^{-16} \mathrm{~m}\) (b) \(1.6 \times 10^{-11} \mathrm{~m}\) (c) \(1.4 \times 10^{-10} \mathrm{~m}\) (d) \(1.4 \times 10^{-11} \mathrm{~m}\)

An electron (mass \(m\) ) with an initial velocity \(\mathbf{v}=v_{0} \hat{\mathbf{i}}\) is in an electric \(\mathbf{E}=E_{0} \hat{\mathbf{j}} .\) If \(\lambda_{0}=h / m v_{0}\), it's de-Broglie wavelength at time \(t\) is given by \(\quad\) (a) \(\lambda_{0}\) (b) \(\lambda_{0} \sqrt{1+\frac{e^{2} E^{2} t^{2}}{m^{2} v_{0}^{2}}}\) (c) \(\frac{\lambda_{\mathrm{D}}}{\sqrt{1+\frac{\mathrm{e}^{2} E_{0^{2}}^{2}}{m^{2} v_{0}^{2}}}}\) (d) \(\frac{\lambda_{0}}{\left(1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}\right)}\)

An electron of mass \(m\) and charge \(e\) initially at rest gets accelerated by a constant electric field \(E\). The rate of change of de-Broglie wavelength of this electron at time \(t\) ignoring relativistic effect is (a) \(\frac{-h}{e E t^{2}}\) (b) \(\frac{-e E t}{E}\) (c) \(\frac{-m h}{e E t^{2}}\) (d) \(\frac{-h}{e E}\)

What should be the velocity of an electron so that its momentum becomes equal to that of a photon of wavelength \(5200 \AA\) ? (a) \(10^{3} \mathrm{~ms}^{-1}\) (b) \(1.2 \times 10^{3} \mathrm{~ms}^{-1}\) (c) \(1.4 \times 10^{3} \mathrm{~ms}^{-1}\) (d) \(2.8 \times 10^{3} \mathrm{~ms}^{-1}\)