An electron (mass \(m\)) with an initial velocity \(v={ v }_{ 0 }\vec { i } ({ v }_{ 0 }>0) \) is an electric field \(v={ v }_{ 0 }\vec { i } ({ v }_{ 0 }>0)\quad \) its de-Broglie wave-length 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?

Which of the following has minimum stopping potential?

What is de-Broglie wavelength associated with electron moving under a potential difference of 10⁴ V. 

An X-ray tube operates at 10KV. The ratio of X-ray wavelength to the de-Broglie wavelength is

The de-Broglie wavelength of the tennis ball of mass 60g moving with a velocity of 10m/s is approximately: (Plank's constant h = \(h=6.63\times { 10 }^{ -34 }Js\)

What is the de-Broglie wavelength of the particle accelerated through a potential difference V? Given, \(h=6.63\times { 10 }^{ -34 }Js\)mass of a nucleon = \(1.66\times { 10 }^{ -27 }kg\)

An electron of mass m and a photon have same energy E.The ratio of de-Broglie wavelengths associated with them is(c being velocity of light)

If v is frequency, \(\lambda \) is the wavelength and \(\overline { v } \) is the wave number then the energy of a photon can be represented by 

An increase in the frequency of the incident light...........the velocity with which photoelectron is ejected.

The minimum frequency required to eject an electron from the surface of a metal is called.............

Photon is not a ......but it is a........

The velocity of photon in different media is.......

The momentum of a photon of energy E is...........and of wavelength \(\lambda \)is......

Name the device that converts changes in intensity illumination into changes in electric current. Give three applications of this device.

An electron and a proton have the same de-Broglie wavelength. Which one these have higher kinetic energy? Which one is moving faster?

(i) For what kinetic energy of a neutron will associated de Broglie wavelength be 1.40 x 10^-10m?
(ii) Also find the de-Broglie wavelength of a neutron in thermal equilibrium with matter,having an average kinetic energy of (3/2) kT and temperature is 300 K.

The two lines marked A and B in the given figure. Show a plot of de-Broglie wavelength \(\lambda \) versus \(\frac { 1 }{ \sqrt { V } } \), where V is the accelerating potential for two nuclei  \(_{ 1 }^{ 2 }{ H }\) and \(_{ 1 }^{ 3 }{ H }\).
(i) What does the slope of the lines represent?
(ii) Identify, which of the lines corresponded to these nuclei.

X-rays fall on a photosensitive surface to cause photoelectric emission. Assuming that the work function of the surface can be neglected, find the relation between the de-Broglie wavelength (\(\lambda \)) of the electrons emitted to the energy (E_v) of the incident photons. Draw the nature of the graph for Aas a function of E_v.

What is the de Broglie wavelength associated with
(a) an electron moving with a speed of 5.4 x 10⁶m/s
(b)a ball of mass 150g travelling at 30.0m/s?

The energy flux of sunlight reaching the surface of the earth is \(1.388\times{ 10 }^{ 3 }w/{ m }^{ 2 }\). 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 nm.

Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons. The second number tells you why our eye can never count photons,even in barely detectable light.
(a) The number of photons emitted per second by an MW transmitter of 10 kW power emitting radio waves of wavelength 500 m.
(b) The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of while light that we humans can perceive (\(\sim \)\({ (10 }^{ -10 }Wm^{ -2 })\). Take the area of the pupil to be white light to be about 0.4 cm² and the average frequency of white light to be about 6 x 10¹⁴ Hz.

Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage.Which probe has greater energy? (For quantitative comparison,take the wavelength of the probe equal to 1\(\overset { \circ }{ A } \), which is of the order of inter-atomic spacing in the lattice), (\({ m }_{ e }=9.11\times{ 10 }^{ -31 }kg.)\)