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NEET 2008
Exam
NEET
Year
2008
Subject
Physics
Chapter
Dual Nature of Matter

NEET 2008 · Physics · Dual Nature of Matter

A particle of mass 1 mg has the same wavelength as an electron...

A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3×106 ms−13 \times 10^6 \mathrm{~ms}^{-1}. The velocity of the particle is (Mass of electron =9.1×10−31 kg=9.1 \times 10^{-31} \mathrm{~kg} )

Options

  1. A2.7×10−18 ms−12.7 \times 10^{-18} \mathrm{~ms}^{-1}
  2. B9×10−2 ms−19 \times 10^{-2} \mathrm{~ms}^{-1}
  3. C3×10−31 ms−13 \times 10^{-31} \mathrm{~ms}^{-1}
  4. D2.7×10−21 ms−12.7 \times 10^{-21} \mathrm{~ms}^{-1}

Correct answer

A. 2.7×10−18 ms−12.7 \times 10^{-18} \mathrm{~ms}^{-1}

Step-by-step solution

Wavelength of a particle is given by λ=hp\lambda=\frac{h}{p} where hh is Planck's constant. and wavelength of an electron is given by λe=hpeλ=λep=pemv=meyey=mevem\begin{aligned} \lambda_e & =\frac{h}{p_e} \\ \lambda & =\lambda_e \\ p & =p_e \\ m v & =m_e y_e \\ y & =\frac{m_e v_e}{m} \end{aligned} So, Putting the undergiven data, we get me=9.1×10−31 kg,ve=3×106 m/sm=1mg=1×10−6 kgy=9.1×10−31×3×1061×10−6=2.7×10−18 ms−1\begin{aligned} & m_e=9.1 \times 10^{-31} \mathrm{~kg}, v_e=3 \times 10^6 \mathrm{~m} / \mathrm{s} \\ & m=1 \mathrm{mg}= 1 \times 10^{-6} \mathrm{~kg} \\ & y=\frac{9.1 \times 10^{-31} \times 3 \times 10^6}{1 \times 10^{-6}} \\ &=2.7 \times 10^{-18} \mathrm{~ms}^{-1} \end{aligned}
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