Advertisements
Advertisements
प्रश्न
An electron and a photon each have a wavelength of 1.00 nm. Find
(a) their momenta,
(b) the energy of the photon, and
(c) the kinetic energy of electron.
Advertisements
उत्तर
Wavelength of an electron (`lambda_"e"`) and a photon `(lambda_"p"), lambda_"e" = lambda_"p" = lambda` = 1 nm = 1 × 10−9 m
Planck’s constant, h = 6.63 × 10−34 Js
(a) The momentum of an elementary particle is given by de Broglie relation:
`lambda = "h"/"p"`
`"p" = "h"/lambda`
It is clear that momentum depends only on the wavelength of the particle. Since the wavelengths of an electron and a photon are equal, both have an equal momentum.
∴ p = `(6.63 xx 10^(-34))/(1 xx 10^(-9))`
= 6.63 × 10−25 kg ms−1
(b) The energy of a photon is given by the relation:
`"E" = "hc"/lambda`
Where,
Speed of light, c = 3 × 108 m/s
∴ E = `(6.63 xx 10^(-34) xx 3 xx 10^8)/(1 xx 10^(-9) xx 1.6 xx 10^(-19)`
= 1243.1 eV
= 1.243 keV
Therefore, the energy of the photon is 1.243 keV.
(c) The kinetic energy (K) of an electron having momentum p,is given by the relation:
`"K" = 1/2 "p"^2/"m"`
Where,
m = Mass of the electron = 9.1 × 10−31 kg
p = 6.63 × 10−25 kg ms−1
∴ K = `1/2 xx (6.63 xx 10^(-25))^2/(9.1 xx 10^(-31))`
= 2.415 × 10−19 J
= `(2.415 xx 10^(-19))/(1.6 xx 10^(-19))`
= 1.51 eV
Hence, the kinetic energy of the electron is 1.51 eV.
संबंधित प्रश्न
Describe the construction of photoelectric cell.
What is the de Broglie wavelength of a dust particle of mass 1.0 × 10−9 kg drifting with a speed of 2.2 m/s?
For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10−10 m?
Find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of `(3/2)` kT at 300 K.
Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
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 Å, which is of the order of inter-atomic spacing in the lattice) (me = 9.11 × 10−31 kg).
Compute the typical de Broglie wavelength of an electron in a metal at 27°C and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10−10 m.
The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
E = hv, p = `"h"/lambda`
But while the value of λ is physically significant, the value of v (and therefore, the value of the phase speed vλ) has no physical significance. Why?
A electron of mass me revolves around a nucleus of charge +Ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated wit it is expressed as `vecμ =−e/(2 m_e)vecL `, where `vec L` is the orbital angular momentum of the electron. Give the significance of negative sign.
Why photoelectric effect cannot be explained on the basis of wave nature of light? Give reasons.
The wavelength of the matter wave is dependent on ______.
A proton and α-particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelength λp to that λα is _______.
An electromagnetic wave of wavelength ‘λ’ is incident on a photosensitive surface of negligible work function. If ‘m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength λd, 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 = c/100`. Then ______.
- `E_e/E_p = 10^-4`
- `E_e/E_p = 10^-2`
- `p_e/(m_ec) = 10^-2`
- `p_e/(m_ec) = 10^-4`
Given below are two statements:
Statement - I: Two photons having equal linear momenta have equal wavelengths.
Statement - II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.
In the light of the above statements, choose the correct answer from the options given below.
The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : `sqrt2`. Then, the ratio of Vp to Vd will be ______.
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
E, c and `v` represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength?
Matter waves are ______.
