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PhysicsModern PhysicsDe Broglie & Matter WavesEasy2 minQB

PhysicsEasynumerical

Passage / Comprehension

Some phenomenon's of light can be explained by wave theory and other some phenomenon's show the particle nature of light. De-Broglie proposed a hypothesis based on the dual nature of light. According to De-Broglie each moving particle consists of a wave. This wave is known as De-Broglie wave or matter wave and its wavelength is given by $λ = \frac{h}{p}$ . Actually, this expression correlate wave and particle nature. ( $λ$ ) represent the wave nature and momentum $(p)$ represent the particle nature.

A proton and $α$ particle have equal kinetic energies. If $λ_{α}$ and $λ_{p}$ are the De-Broglie wavelengths of $α$ particle and proton, then the ratio of $\frac{λ _{α}}{λ _{p}}$ is found to be $α / β$ , where $α$ and $β$ are least integers. Find the value of $(α + β)$ .

Answer:

3.00

Solution:

$\frac{λ _{α}}{λ _{p}} = \frac{m _{p}}{m _{α}} = \frac{1}{4} = \frac{1}{2}$

So $α + β = 1 + 2 = 3$

Answer 3.00

Stream:JEESubject:PhysicsTopic:Modern PhysicsSubtopic:De Broglie & Matter Waves

⏱ 2mℹ️ Source: QB

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