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19/08/2021 10:37 am
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The velocity of particle A is 0.1 ms–1 and that of particle B is 0.05 ms–1. If the mass of particle B is five times that of particle A, then the ratio of de Broglie wavelengths associated with the particles A and B is
(a) 2 : 5
(b) 3 : 4
(c) 6 : 4
(d) 5 : 2
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19/08/2021 10:48 am
Correct answer: (d) 5 : 2
Explanation:
Given, vA = 0.1 ms–1 and vB = 0.05 ms–1 also, mB = 5mA
de-Broglie wavelength, λ = \(\frac{h}{mv}\)
∴ \(\frac{\lambda_A}{\lambda_B}\) = \(\frac{\frac{h}{m_Av_A}}{\frac{h}{m_Bv_B}}\)
= \(\frac{m_Bv_B}{m_Av_A}\)
= \(\frac{5m_A \times 0.05}{m_A \times 0.1}\)
= 5 x 0.5 = \(\frac{5}{2}\)
∴ λA = λB = 5:2