A particle is dropped from a height $H$. The de-Broglie wavelength of the particle as a function of height is proportional to

The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly

Consider a beam of electrons (each electron with energy $E_0$ ) incident on a metal surface kept in an evacuated chamber. Then,

Consider figure given below. Suppose the voltage applied to $A$ is increased. The diffracted beam will have the maximum at a value of $\theta$ that

A proton, a neutron, an electron and an $\alpha$-particle have same energy. Then, their de-Broglie wavelengths compare as

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

An electron (mass $m$ ) with an initial velocity $\mathbf{v}=v_0 \mathbf{i}\left(v_0>0\right)$ is in an electric field $\mathbf{E}=-E_0 \hat{\mathbf{i}}\left(E_0=\right.$ constant $\left.>0\right)$. It's de-Broglie wavelength at time $t$ is given by

An electron (mass $m$ ) with an initial velocity $\mathbf{v}=v_0 \hat{\mathbf{i}}$ is in an electric field $\mathbf{E}=E_0 \hat{\mathbf{j}}$. If $\lambda_0=h / m v_0$, it's de-Broglie wavelength at time $t$ is given by

Relativistic corrections become necessary when the expression for the kinetic energy $\frac{1}{2} m v^2$, becomes comparable with $m c^2$, where $m$ is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron?

Two particles $A_1$ and $A_2$ of masses $m_1, m_2\left(m_1>m_2\right)$ have the same de-Broglie wavelength. Then,

The de-Broglie wavelength of a photon is twice, the de-Broglie wavelength of an electron. The speed of the electron is $v_e=\frac{c}{100}$. Then,

Photons absorbed in matter are converted to heat. A source emitting $n$ photon $/ \mathrm{sec}$ of frequency $v$ is used to convert 1 kg of ice at $0^{\circ} \mathrm{C}$ to water at $0^{\circ} \mathrm{C}$. Then, the time $T$ taken for the conversion

A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de-Broglie wavelength of the particle varies cyclically between two values $\lambda_1, \lambda_2$ with $\lambda_1>\lambda_2$. Which of the following statement are true?

A proton and an $\alpha$-particle are accelerated, using the same potential difference. How are the de-Broglie wavelengths $\lambda_p$ and $\lambda_\alpha$ related to each other?

(i) In the explanation of photoeletric effect, we assume one photon of frequency $v$ collides with an electron and transfers its energy. This leads to the equation for the maximum energy $E_{\text {max }}$ of the emitted electron as

$$E_{\max }=h v-\phi_0$$

where $\phi_0$ is the work function of the metal. If an electron absorbs 2 photons (each of frequency $v$ ), what will be the maximum energy for the emitted electron?

(ii) Why is this fact (two photon absorption) not taken into consideration in our discussion of the stopping potential?

There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength.

Do all the electrons that absorb a photon come out as photoelectrons?

There are two sources of light, each emitting with a power of 100 W . One emits X-rays of wavelength 1 nm and the other visible light at 500 nm . Find the ratio of number of photons of $X$-rays to the photons of visible light of the given wavelength?

Consider figure for photoemission. How would you reconcile with momentum-conservation? Note light (photons) have momentum in a different direction than the emitted electrons.

Consider a metal exposed to light of wavelength 600 nm . The maximum energy of the electron doubles when light of wavelength 400 nm is used. Find the work function in eV.

Assuming an electron is confined to a 1 nm wide region, find the uncertainty in momentum using Heisenberg uncertainty principle $(\Delta x \times \Delta p \approx h)$. You can assume the uncertainty in position $\Delta x$ as 1 nm . Assuming $p \approx \Delta p$, find the energy of the electron in electronvolts.

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 make about their frequencies?

Two particles $A$ and $B$ of de-Broglie wavelengths $\lambda_1$ and $\lambda_2$ combine to form a particle $C$. The process conserves momentum. Find the de-Broglie wavelength of the particle $C$. (The motion is one-dimensional)

A neutron 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 $\theta=30 \Upsilon$. What is the kinetic energy $E$ of the beam in eV ?

Consider a thin target $\left(10^{-2} \mathrm{~m}\right.$ square, $10^{-3} \mathrm{~m}$ thickness) of sodium, which produces a photocurrent of $100 \propto \mathrm{~A}$ when a light of intensity 100 $\mathrm{W} / \mathrm{m}^2(\lambda=660 \mathrm{~nm})$ falls on it. Find the probability that a photoelectron is produced when a photon strikes a sodium atom. [Take density of $\mathrm{Na}=0.97 \mathrm{~kg} / \mathrm{m}^3$ ]

Consider an electron in front of metallic surface at a distance $d$ (treated as an infinite plane surface). Assume the force of attraction by the plate is given as $\frac{1}{4} \frac{q^2}{4 \pi \varepsilon_0 d^2}$. Calculate work in taking the charge to an infinite distance from the plate. Taking $d=0.1 \mathrm{~nm}$, find the work done in electron volts. [Such a force law is not valid for $d<0.1 \mathrm{~nm}$ ]

A student performs an experiment on photoelectric effect, using two materials $A$ and $B$. A plot of $V_{\text {stop }}$ versus $v$ is given in figure.

(i) Which material $A$ or $B$ has a higher work function?

(ii) Given the electric charge of an electron $=1.6 \times 10^{-19} C$, find the value of $h$ obtained from the experiment for both $A$ and $B$.

Comment on whether it is consistent with Einstein's theory.

A particle $A$ with a mass $m_A$ is moving with a velocity $v$ and hits a particle $B$ (mass $m_B$ ) at rest (one dimensional motion). Find the change in the de-Broglie wavelength of the particle $A$. Treat the collision as elastic.

Consider a 20 W bulb emitting light of wavelength $5000 \mathop A\limits^o$ and shining on a metal surface kept at a distance 2 m . Assume that the metal surface has work function of 2 eV and that each atom on the metal surface can be treated as a circular disk of radius $1.5 \mathop A\limits^o$.

(i) Estimate number of photons emitted by the bulb per second. [Assume no other losses]

(ii) Will there be photoelectric emission?

(iii) How much time would be required by the atomic disk to receive energy equal to work function ( 2 eV )?

(iv) How many photons would atomic disk receive within time duration calculated in (iii) above?

(v) Can you explain how photoelectric effect was observed instantaneously?