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18/08/2021 10:57 am
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Two fast moving particles X and Y are associated with de Broglie wavelengths 1 nm and 4 nm respectively. If mass of X is nine times the mass of Y, the ratio of kinetic energies of X and Y would be
(a) 3 : 1
(b) 9 : 1
(c) 5 : 12
(d) 16 : 9
1 Answer
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18/08/2021 11:03 am
Correct answer: (d) 16 : 9
Explanation:
de Broglie wavelength λ = \(\frac{h}{mv}\)
\(\frac{λ_1}{λ_2}\) = \(\frac{m_2v_2}{m_1v_1}\); \(\frac{1}{4}\)
= \(\frac{1}{9}\) x \(\frac{v_2}{v_1}\)
\(\frac{v_2}{v_1}\) = \(\frac{9}{4}\); \(\frac{v_1}{v_2}\) = \(\frac{4}{9}\)
KE = \(\frac{1}{2}mv^2\)
\(\frac{KE_1}{KE_2}\) = \(\frac{m_1}{m_2}\) x \(\frac{v_1^2}{v_2^2}\)
= \(\frac{9}{1}\) x \((\frac{4}{9})^2\)
= \(\frac{16}{9}\)