Davisson-Germer, Uncertainty, Compton & X-Rays

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R

Assertion A: The beam of electrons show wave nature and exhibit interference and diffraction. Reason R: Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements, choose the most appropriate answer from the options given below:

The minimum wavelength of $X$-rays produced by an electron accelerated through a potential difference of $V$ volts is proportional to:

Given below are two statements:

Statement I: Davisson-Germer experiment establishes the wave nature of electrons. Statement II: If electrons have wave nature, they can interfere and show diffraction. In the light of the above statements choose the correct answer from the option given below:

Given below are two statements: one is labeled as Assertion A and the other is labelled as Reason R.

Assertion A: An electron microscope can achieve better resolving power than an optical microscope.

Reason R: The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light.

In the light of the above statements, choose the correct answer from the options given below:

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:

The speed of electrons in a scanning electron microscope is 1 $\times$ 107 ms-1. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of:

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases is the same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-

An electron having de-Broglie wavelength $\lambda$ is incident on a target in a X-ray tube. Cut-off wavelength of emitted X-ray is:

The wave nature of electrons was experimentally verified by,

A beam of electrons of energy E scatters from a target having atomic spacing of 1 $\text{\AA}$. The first maximum intensity occurs at $\theta$ = 60o. Then E (in eV) is ______.

(Planck constant h = 6.64 × 10–34 Js,

1 eV = 1.6 × 10–19 J, electron

mass m = 9.1 × 10–31 kg)

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10–12 m, the minimum electron energy required is close to -

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X– rays. It produces continuous as well as characteristic X-rays. If $\lambda$min is the smallest possible wavelength of X-ray in the spectrum, the variation of log$\lambda$min with log V is correctly represented in:

Electrons of mass m with de-Broglie wavelength $\lambda$ fall on the target in an X-ray tube. The cutoff wavelength ($\lambda$0) of the emitted X-ray is

Match List - $\text{I}$ (Fundamental Experiment) with List - $\text{II}$ (its conclusion) and select the correct option

from the choices given below the list:

A parallel beam of electrons travelling in x-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum py in the y-direction then for a majority of electrons passing through the slit (h is Planck's constant):

Match List - I (Experiment performed) with List - II (Phenomena discovered/associated) and select

the correct option from the options given below the lists:

A photon of wavelength $\lambda$ is scattered from an electron, which was at rest. The wavelength shift $\Delta\lambda$ is three times of $\lambda$ and the angle of scattering $\theta$ is 60o. The angle at which the electron recoiled is $\phi$. The value of tan $\phi$ is: (electron speed is much smaller than the speed of light)

A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?

This question has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement 1: Davisson - Germer experiment established the wave nature of electrons. Statement 2: If electrons have wave nature, they can interfere and show diffraction.

In the Davisson and Germer experiment, the velocity of electrons emitted from the electron gun can be increased by

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).

Electrons accelerated by potential $V$ are diffracted from a crystal. If $d = 1\text{ \AA}$ and $i = 30^\circ,\ V$ should be about

$\left(h = 6.6 \times 10^{-34}\text{ Js},\ m_e = 9.1 \times 10^{-31}\text{ kg},\ e = 1.6 \times 10^{-19}\text{ C}\right)$

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).

If a strong diffraction peak is observed when electrons are incident at an angle $'i'$ from the normal to the crystal planes with distance $'d'$ between them (see figure), de Broglie wavelength $\lambda_{dB}$ of electrons can be calculated by the relationship ($n$ is an integer)

In an experiment, electrons are made to pass through a narrow slit of width $'d'$ comparable to their de Broglie wavelength. They are detected on a screen at a distance $'D'$ from the slit (see figure).

Which of the following graphs can be expected to represent the number of electrons $'N'$ detected as a function of the detector position $'y'\ (y = 0$ corresponds to the middle of the slit $)$

The minimum wavelength of the X-rays produced by electrons accelerated through a potential difference of $V$ volts is directly proportional to