Advertisements
Advertisements
प्रश्न
Two neutral particles are kept 1 m apart. Suppose by some mechanism some charge is transferred from one particle to the other and the electric potential energy lost is completely converted into a photon. Calculate the longest and the next smaller wavelength of the photon possible.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Advertisements
उत्तर
Given:-
Distance between the two neutral particles, r = 1 m
Electric potential energy,
`E_1 = (kq^2)/r = kq^2`
where `K = 1/(4pi∈_0)`
Energy of photon,
`E_2 = (hc)/λ`,
where λ = wavelength of light
h = Planck's constant
c = speed of light
Here, E1 = E2
`therefore kq^2 = (hc)/λ`
`⇒ λ = (hc)/(kq^2)`
For wavelength, λ, to be maximum, charge q should be minimum.
`q = e = 1.6 xx 10^-19 "C"`
Maximum wavelength,
`λ = (hc)/(kq^2)`
`= (6.63 xx 3 xx 10^-34 xx 10^8)/(9 xx 10^2 xx (1.6)^2 xx 10^-38)`
`= 0.863 xx 10^3 = 863 "m"`
Next smaller wave length,
`λ = (6.63 xx 3 xx 10^-34 xx 10^8)/(9 xx 10^4 xx 4 xx (1.6)^2 xx 10^-38)`
`= 863/4`
`= 215.74 "m"`
APPEARS IN
संबंधित प्रश्न
(a) A monoenergetic electron beam with electron speed of 5.20 × 106 m s−1 is subject to a magnetic field of 1.30 × 10−4 T normal to the beam velocity. What is the a radius of the circle traced by the beam, given e/m for electron equals 1.76 × 1011 C kg−1?
(b) Is the formula you employ in (a) valid for calculating the radius of the path of a 20 MeV electron beam? If not, in what way is it modified?
Is the formula you employ in (a) valid for calculating radius of the path of a 20 MeV electron beam? If not, in what way is it modified?
An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure (∼10−2 mm of Hg). A magnetic field of 2.83 × 10−4 T curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the ‘fine beam tube’ method. Determine e/m from the data.
A photographic film is coated with a silver bromide layer. When light falls on this film, silver bromide molecules dissociate and the film records the light there. A minimum of 0.6 eV is needed to dissociate a silver bromide molecule. Find the maximum wavelength of light that can be recorded by the film.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
A horizontal cesium plate (φ = 1.9 eV) is moved vertically downward at a constant speed v in a room full of radiation of wavelength 250 nm and above. What should be the minimum value of v so that the vertically-upward component of velocity is non-positive for each photoelectron?
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
In an experiment on photoelectric effect, the emitter and the collector plates are placed at a separation of 10 cm and are connected through an ammeter without any cell. A magnetic field B exists parallel to the plates. The work function of the emitter is 2.39 eV and the light incident on it has wavelengths between 400 nm and 600 nm. Find the minimum value of B for which the current registered by the ammeter is zero. Neglect any effect of space charge.
A silver ball of radius 4.8 cm is suspended by a thread in a vacuum chamber. Ultraviolet light of wavelength 200 nm is incident on the ball for some time during which light energy of 1.0 × 10−7 J falls on the surface. Assuming that on average, one photon out of every ten thousand is able to eject a photoelectron, find the electric potential at the surface of the ball, assuming zero potential at infinity. What is the potential at the centre of the ball?
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Plot a graph to show the variation of stopping potential with frequency of incident radiation in relation to photoelectric effect.
The stopping potential in an experiment on photoelectric effect is 1.5V. What is the maximum kinetic energy of the photoelectrons emitted? Calculate in Joules.
Answer the following question.
Why is the wave theory of electromagnetic radiation not able to explain the photoelectric effect? How does a photon picture resolve this problem?
In the case of a photo electric effect experiment, explain the following facts, giving reasons.
The wave theory of light could not explain the existence of the threshold frequency.
In Photoelectric effect ______.
For a given frequency of light and a positive plate potential in the set up below, If the intensity of light is increased then ______.
In various experiments on photo electricity, the stopping potential for a given frequency of the incident radiation is ______.
The electromagnetic theory of light failed to explain ______.
