Question

In which of the following situations, the heavier of the two particles has smaller de Broglie wavelength? The two particles
(a) move with the same speed
(b) move with the same linear momentum
(c) move with the same kinetic energy
(d) have fallen through the same height

Answer 1

Answer:

If the two particles moves with same speed then  the heavier of the two particles has smaller de Broglie wavelength, as on that situation wavelength is inversely proportional to the mass of the particle. that's why heavier elements has smaller wavelength.

Explanation:

Answer 2

The correct answers are options (a), (c) and (d).

EXPLANATION:

• Let the heavier particle has the mass, m1 and the lighter particle has mass, m2.
• When both the particles move with the same speed v, the heavier particle’s de Broglie wavelength,
• λ1 = hm1v   …(1)
• The lighter particle’s de Broglie wavelength,
• λ2 = hm2v   …(2)
• So, we can say that λ1 < λ2. Thus, the correct answer is option (a).
• When they move with the same linear momentum, then when de Broglie relation is used, λ = hp.
• It can be found that same wavelengths are there in the both. So, option (b) is incorrect.
• The heavier particle’s de Broglie wavelength, λ1 = h2m1K. The lighter particle’s de Broglie wavelength, λ2 = h2m2K.
• If m1>m2, then λ1<λ2.
• So, option (c) is correct.
• When they have dropped via the same height h, then both the bodies have the velocity, v = 2gh
• Now,
• λ1 = hm12gh
• λ2 = hm22gh
• m1>m2
• Therefore, λ1<λ2
• So, option (d) is correct.