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प्रश्न
Which of the following graphs correctly represents the variation of a particle momentum with its associated de-Broglie wavelength?
पर्याय
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उत्तर
Explanation:
de-Broglie wavelength is the wavelength that is connected to an object in relation to its momentum and mass. Typically, the force of a particle is inversely proportional to its de-Broglie wavelength.
A photon's momentum is determined by:
P = `E/c = h/lambda` where E is the energy of the photon, c is the speed of light in vacuum, h is Planck's constant and λ is the de-Broglie wavelength.
According to de-Broglie, `p = h/lambda` or `p ∝ 1/lambda`.
By this relation, we can conclude that the linear momentum of a photon is inversely proportional to the de-Broglie wavelength. The graph of p vs λ shall be a rectangular hyperbola.
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 dust particle of mass 1.0 × 10−9 kg drifting with a speed of 2.2 m/s?
Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
What is the de Broglie wavelength of a nitrogen molecule in air at 300 K? Assume that the molecule is moving with the root-mean square speed of molecules at this temperature. (Atomic mass of nitrogen = 14.0076 u)
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 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 (v_0 > 0)` is in an electric field `E = - E_0hati `(E0 = constant > 0). It’s de Broglie wavelength at time t is given by ______.
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 De-Broglie wavelength of electron in the third Bohr orbit of hydrogen is ______ × 10-11 m (given radius of first Bohr orbit is 5.3 × 10-11 m):
