Dual Nature of Radiation

An electron, a doubly ionized helium ion (He++) and a proton are having the same kinetic energy.
The relation between their respective de-Broglie wavelengths \(\lambda\)e, \(\lambda\)He++ and \(\lambda\)p is :

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength
of nitrogen molecule is close to :
(Given : nitrogen molecule weight : 4.64 \(\times\) 10–26 kg, Boltzman
constant: 1.38 \(\times\) 10–23...

A beam of electrons of energy E scatters from
a target having atomic spacing of 1 \(\mathop A\limits^o\). 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 ×...

The surface of a metal is illuminated alternately
with photons of energies E1 = 4 eV and E2 = 2.5 eV
respectively. The ratio of maximum speeds of the
photoelectrons emitted in the two cases is 2. The
work function of the metal in (eV) is __...

Given figure shows few data points in a phot electric effect experiment for a certain metal. The
minimum energy for ejection of electron from its surface is: (Plancks constant h = 6.62 × 10–34 J.s)

Particle A of mass mA = \({m \over 2}\) moving along the x-axis with velocity v0 collides elastically with another particle B at rest having mass mB = \({m \over 3}\). If both particles move along the x-axis after the collision, the change ...

In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength
obtained is shown in the figure. As the intensity of incident radiation is increased :

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the
maximum kinetic energy of the photoelectrons becomes three times larger. The work function of
the metal is close to :

Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of
photons of X-rays to the number density of pho...

When radiation of wavelength \(\lambda\) is used to
illuminate a metallic surface, the stopping
potential is V. When the same surface is
illuminated with radiation of wavelength 3\(\lambda\),
the stopping potential is
\({V \over 4}\). If ...

A particle is moving 5 times as fast as an
electron. The ratio of the de-Broglie wavelength
of the particle to that of the electron is 1.878 \(\times\)
10–4. The mass of the particle is close to

Surface of certain metal is first illuminated with light of wavelength \(\lambda\)1 = 350 nm and then, by light of wavelength \(\lambda\)2 = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a fa...

The magnetic field associated with a light wave is given, at the origin, by B = B0 [sin(3.14 \(\times\) 107)ct + sin(6.28 \(\times\) 107)ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maxim...

The electric field of light wave is given as
\($\overrightarrow E = {10^{ - 3}}\cos \left( {{{2\pi x} \over {5 \times {{10}^{ - 7}}}} - 2\pi \times 6 \times {{10}^{14}}t} \right)\mathop x\limits^ \wedge {{\rm N} \over C}\)$

This
light f...

A particle 'P' is formed due to a completely
inelastic collision of particles 'x' and 'y' having
de-Broglie wavelengths '\(\lambda\)x' and '\(\lambda\)y'
respectively. If x and y were moving in opposite
directions, then the de-Broglie wav...

Two particles move at right angle to each other.
Their de-Broglie wavelengths are \(\lambda _1\) and \(\lambda _2\)
respectively. The particles suffer perfectly
inelastic collision. The de-Broglie wavelength
\(\lambda _2\) of the final part...

A nucleus A, with a finite de-broglie
wavelength \(\lambda\)A, undergoes spontaneous fission
into two nuclei B and C of equal mass. B flies
in the same direction as that of A, while C flies
in the opposite direction with a velocity equal
t...

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $${{{\lambda ...

In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :

When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping
potential for the current is –V0/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential i...

The stopping potential V0 (in volt) as a function of frequency (\(\upsilon\)) for a sodium emitter, is shown in the figure.
The work function of sodium, from the data plotted in the figure, will be: (Given: Planck’s constant (h) = 6.63 × 1...

If the de Broglie wavelength of an electron is equal to the 10–3 times the wavelength of a photon of frequency 6 \(\times\) 1014 Hz, then the speed of electron is equal to : (Speed of light = 3 \(\times\) 108 m/s, Planck's constant =...

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to: (\({{{hc} \over e}}\) = 1240 nm eV)

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 -

A metal plate of area 1 \(\times\) 10–4 m2 is illuminated by a radiation of intensity 16 mW/m2. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons.
The number of...

In a photoelectric effect experiment the
threshold wavelength of the light is 380 nm. If
the wavelentgh of incident light is 260 nm, the
maximum kinetic energy of emitted electrons
will be:
Given E (in eV) = 1237/\(\lambda\) (in nm)

A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is :
[Given Planck's constant h = 6.6 × 10–34 Js, speed of light c = 3.0 × 108
m/s]

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths \(\lambda\)N, \(\lambda\)A respectively. The ratio \({{{}^\lambda N} \over {{}^\lambda A}}\)...

The de-Broglie wavelength (\(\lambda\)B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (\(\lambda\)G) by :

Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are \({\lambda _1}\) and \({\lambda _2},\) their de Broglie wavelength in the frame of reference attached to their cent...

If the de Broglie wavelengths associated with a proton and an \(\alpha\)-particle are equal, then the ratio of velocities of the proton and the \(\alpha\)-particle will be :

A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are :
[Take Planck's constant h \(=\) 6.62 \(\times\) 10\(-\)34 ...

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The
collision is head on, and elastic. The ratio of the de-Broglie wavelengths \({\lambda _A}\) to \({\lambda _B}\) after the collision i...

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...

When photons of wavelength \({\lambda _1}\) are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength \({\lambda _2}\) are used, the corresponding stopping potential was thrice tha...

A photoelectric surface is illuminated successively by monochromatic light of wavelengths \(\lambda\) and \({\lambda \over 2}.\) If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first c...

Radiation of wavelength \(\lambda ,\) is incident on a photocell. The fastest emitted electron has speed \(v.\) If the wavelength is changed to \({{3\lambda } \over 4},\) the speed of the fastest emitted electron will be:

Match List - \({\rm I}\) (Fundamental Experiment) with List - \({\rm II}\) (its conclusion) and select the correct option from the choices given below the list:

The anode voltage of a photocell is kept fixed. The wavelength \(\lambda\) of the light falling on the cathode is gradually changed. The plate current \(I\) of the photocell varies as follows :

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. Stat...

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 - \(1\) : A metallic surface is irradiated by a monochromatic light...

Statement - \(1\) : When ultraviolet light is incident on a photocell, its stopping potential is \({V_0}\) and the maximum kinetic energy of the photoelectrons is \({K_{\max }}\). When the ultraviolet light is replaced by \(X\)-rays, both...

If a source of power \(4kW\) produces \({10^{20}}\) photons/second, the radiation belongs to a part of the spectrum called

The surface of a metal is illuminated with the light of \(400\) \(nm.\) The kinetic energy of the ejected photoelectrons was found to be \(1.68\) \(eV.\) The work function of the metal is : \(\left( {hc = 1240eV.nm} \right)\)

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 ca...

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 electro...

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 electro...

Photon of frequency \(v\) has a momentum associated with it. If \(c\) is the velocity of light, the momentum is

The anode voltage of a photocell is kept fixed. The wavelength \(\lambda\) of the light falling on the cathode is gradually changed. The plate current \({\rm I}\) of the photocell varies as follows