Question

A particle of mass \[M\]at rest decays into two masses \[{m_1}\] and\[{m_2}\] with non-zero velocities. The ratio \[\dfrac{{{\lambda _1}}}{{{\lambda _2}}}\] of de Broglie wavelengths of particles is
A. \[\dfrac{{{m_2}}}{{{m_1}}}\]
B. \[\dfrac{{{m_1}}}{{{m_2}}}\]
C. \[\dfrac{{\sqrt {{m_1}} }}{{\sqrt {{m_2}} }}\]
D. \[1:1\]

Answer 1

Hint: From the outcome of de Broglie, we capture that for a molecule with analyzed force, p could have a one of a kind charge for its de Broglie frequency might be resolved (and subsequently a particular shade of the mild). Thus the frequency of electromagnetic radiation is indistinguishable from the de-Broglie frequency

Formula used:
\[P = mv\]
Here, \[P\] is the momentum of the particle,
\[m\] is the mass of the particle,
\[v\] is the speed of the particle

Complete step by step answer:
By conservation of momentum,
\[mv = {m_1}{v_1} + {m_2} + {v_2}\]
As mass \[m\] is at rest
So we can write it as, \[v = 0\]
Thus we get
\[{m_1}{v_1} = - {m_2}{v_2}\]
It indicates the magnitude of momentum of masses is the same I.e. \[{p_1} = {p_2}\]
So, De Broglie wavelengths of masses \[{m_1}\] and \[{m_2}\] are \[{\lambda _1} = \dfrac{h}{{{p_1}}}\] and \[{\lambda _2} = \dfrac{h}{{{p_2}}}\]
Thus, \[\dfrac{{{\lambda _1}}}{{{\lambda _2}}} = \dfrac{{{p_1}}}{{{p_2}}} = 1 \text{or} 1:1\]

Hence, the correct answer is option (D).

Additional information:
• Light carries on particularly like a wave anyway it can moreover be considered to incorporate little projects of energy known as photons.
• Photons supply a set measure of intensity anyway and have no mass.
• The dating among force and frequency is indispensable for all garbage. Matter-wave speaks to the chance of finding a molecule in territory.
• Matter waves are not electromagnetic in nature. De-Broglie or remember wave is impartial of the cost on the fabric molecule.
• School undergrads ought to perceive the basic homes of mellow, comprehensive of brilliance, conceals, and being seen.
• Every minuscule molecule, regardless of whether mass less, similar to photons, or having mass, similar to electrons, have wave properties.
• The connection among force and frequency is central for all particles. All issues are made out of tiny particles which can exist autonomously. Particles of the issue have spaces between them. Particles of the issue are ceaselessly moving. Particles of issue pull in one another.

Note: De Broglie wave, likewise called matter wave, any part of the conduct or properties of a material item that shifts as expected or space in similarity with the numerical conditions that depict waves.
The hypothesis that light carries on both as a wave and as a molecule. It can create diffraction and impedance designs which must be clarified utilizing waves.