A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3 × 106 m s ⁻¹. The velocity of the particle is (a) 3 × 10 - 31 ms ⁻¹ (b) 2.7 × 10⁻²¹ m s⁻¹ (c) 2.7 × 10 - 18 ms ⁻¹ (d) 9 × 10 - 2 ms ⁻¹

Answer: (c). Same λ = h/mv means same momentum: m v = me ve. m = 1 mg = 10⁻⁶ kg v = 9.1 × 10⁻³¹ × 3 × 10⁶10⁻⁶ = 2.7 × 10⁻¹⁸ m s⁻¹ So the answer is (c).

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Matter Waves: de Broglie Wavelength

A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3 $\times$ 106 m s ${}^{-1}$ . The velocity of the particle is

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Answer: (c)

Same $\lambda = \dfrac{h}{mv}$ means same momentum: $m v = m_e v_e$ .
$m = 1\text{ mg} = 10^{-6}\text{ kg}$
$v = \dfrac{9.1 \times 10^{-31} \times 3 \times 10^{6}}{10^{-6}} = 2.7 \times 10^{-18}\text{ m s}^{-1}$
So the answer is (c).

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