Advertisements
Advertisements
प्रश्न
Relativistic corrections become necessary when the expression for the kinetic energy `1/2 mv^2`, becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?
- λ = 10 nm
- λ = 10–1 nm
- λ = 10–4 nm
- λ = 10–6 nm
पर्याय
a and c
a and d
c and d
a and b
Advertisements
उत्तर
c and d
Explanation:
De-Broglie or matter wave is independent of die charge on the material particle. It means matter wave of the de-Broglie wave is associated with every moving particle (whether charged or uncharged).
The de-Broglie wavelength at which relativistic corrections become important is that the phase velocity of the matter waves can be greater than the speed of the light (3 × 108 m/s).
The wavelength of de-Broglie wave is given by λ = h/p = h/mv
Here, h = 6.6 × 10-34 Js
And for electron, m = 9 × 10-31 kg
To approach these types of problems we use the hit and trial method by picking up each option one by one.
In option (a), λ1 = 10 nm = 10 × 10–9 m = 10–8 m
⇒ `v_1 = (6.6 xx 10^-34)/((9 xx 10^-31) xx 10^-8)`
= `2.2/3 xx 10^5 = 10^5` m/s
In option (b), λ2 = 10–1 nm = 10–1 × 10–9 m = 10–10 m
⇒ `v_2 = (6.6 xx 10^-34)/((9 xx 10^-31) xx 10^-10) = 10^7` m/s
In option (c), λ3 = 10–4 nm = 10–4 × 10–9 m = 10–13 m
⇒ `v_3 = (6.6 xx 10^-34)/((9 xx 10^-31) xx 10^-13) = 10^10` m/s
In option (d), λ4 = 10–6 nm = 10–6 × 10–9 m = 10–15 m
⇒ `v_4 = (6.6 xx 10^-34)/((9 xx 10^-31) xx 10^-15) = 10^12` m/s
Thus options (c) and (d) are correct as v3 and v4 is greater than 3 × 108 m/s.
APPEARS IN
संबंधित प्रश्न
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 wavelength λ of a photon and the de-Broglie wavelength of an electron have the same value. Show that energy of a photon in (2λmc/h) times the kinetic energy of electron; where m, c and h have their usual meaning.
Sodium and copper have work function 2.3 eV and 4.5 eV respectively. Then, the ratio of the wavelengths is nearest to ______.
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 ______
A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.
Two particles A1 sand A2 of masses m1, m2 (m1 > m2) have the same de Broglie wavelength. Then ______.
- their momenta are the same.
- their energies are the same.
- energy of A1 is less than the energy of A2.
- energy of A1 is more than the energy of A2.
A proton and an α-particle are accelerated, using the same potential difference. How are the de-Broglie wavelengths λp and λa related to each other?
Two particles A and B of de Broglie wavelengths λ1 and λ2 combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).
An electron is accelerated from rest through a potential difference of 100 V. Find:
- the wavelength associated with
- the momentum and
- the velocity required by the electron.
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.
Two particles move at a right angle to each other. Their de-Broglie wavelengths are λ1 and λ2 respectively. The particles suffer a perfectly inelastic collision. The de-Broglie wavelength λ, of the final particle, is given by ______.
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 ______.
An electron of mass me, and a proton of mass mp = 1836 me are moving with the same speed. The ratio of the de Broglie wavelength `lambda_"electron"/lambda_"proton"` will be:
For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
How will the de-Broglie wavelength associated with an electron be affected when the velocity of the electron decreases? Justify your answer.
E, c and `v` represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength?
