Advertisements
Advertisements
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.
Advertisements
उत्तर
Temperature, T = 27°C = 27 + 273 = 300 K
Mean separation between two electrons, r = 2 × 10−10 m
De Broglie wavelength of an electron is given as:
`lambda = "h"/sqrt(3"mkT")`
Where,
h = Planck’s constant = 6.6 × 10−34 Js
m = Mass of an electron = 9.11 × 10−31 kg
k = Boltzmann constant = 1.38 × 10−23 J mol−1 K−1
∴ `lambda = (6.6 xx 10^(-34))/sqrt(3 xx 9.11 xx 10^(-31) xx 1.38 xx 10^(-23) xx 300)`
≈ 6.2 × 10−9 m
Hence, the de Broglie wavelength is much greater than the given inter-electron separation.
APPEARS IN
संबंधित प्रश्न
The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which
(a) an electron, and
(b) a neutron, would have the same de Broglie wavelength.
What is the de Broglie wavelength of a ball of mass 0.060 kg moving at a speed of 1.0 m/s?
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).
State any one phenomenon in which moving particles exhibit wave nature.
Describe briefly how the Davisson-Germer experiment demonstrated the wave nature of electrons.
What are matter waves?
70 cal of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the gas through the same range at constant volume will be (assume R = 2 cal/mol-K).
A proton and α-particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelength λp to that λα is _______.
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.
An electron (mass m) with an initial velocity `v = v_0hati` is in an electric field `E = E_0hatj`. If λ0 = h/mv0, it’s de Broglie wavelength at time t is given by ______.
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.
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 ______.
E, c and `v` represent the energy, velocity and frequency of a photon. Which of the following represents its wavelength?
Matter waves are ______.
The graph which shows the variation of `(1/lambda^2)` and its kinetic energy, E is (where λ is de Broglie wavelength of a free particle):
