The momentum of three microparticles A, B, and C are the same and their mass ratio is 1: 3: 5. The ratio of their de-Broglie wavelength is
Question
The momentum of three microparticles A, B, and C are the same and their mass ratio is 1: 3: 5. The ratio of their de-Broglie wavelength is
Solution
The de-Broglie wavelength (λ) is given by the equation:
λ = h/p
where h is Planck's constant and p is the momentum of the particle.
Given that the momentum (p) of the three particles A, B, and C is the same, the de-Broglie wavelength will be inversely proportional to their masses.
So, if the mass ratio is 1:3:5, the de-Broglie wavelength ratio will be the inverse, i.e., 1/1 : 1/3 : 1/5.
To simplify this ratio, we can multiply each term by 15 (the least common multiple of 1, 3, and 5), which gives us:
15:5:3
So, the ratio of the de-Broglie wavelengths of the three particles A, B, and C is 15:5:3.
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