Dual Nature of Radiation and Matter - Result Question 14

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15. A particle of mass $1 mg$ has the same wavelength as an electron moving with a velocity of $3 \times 10^{6}$ $ms^{-1}$. The velocity of the particle is:

======= ####15. A particle of mass $1 mg$ has the same wavelength as an electron moving with a velocity of $3 \times 10^{6}$ $ms^{-1}$. The velocity of the particle is:

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/dual-nature-of-radiation-and-matter/dual-nature-of-radiation-and-matter—result-question-14.md (a) $2.7 \times 10^{-18} ms^{-1}$

(b) $9 \times 10^{-2} ms^{-1}$

(c) $3 \times 10^{-31} ms^{-1}$

(d) $2.7 \times 10^{-21} ms^{-1}$

[2008] (mass of electron $=9.1 \times 10^{-31} kg$ )

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Answer:

Correct Answer: 15. (a)

Solution:

  1. (a) Wavelength of particle

$ (\lambda_1)=\frac{h}{mv}=\frac{h}{(1 \times 10^{-6}) \times v} $

where $v$ is the velocity of the particle.

Wave length of electron,

$ (\lambda_2)=\frac{h}{(9.1 \times 10^{-31}) \times(3 \times 10^{6})} $

But $\lambda_1=\lambda_2$ (Given)

$ \begin{aligned} & \therefore \frac{h}{(1 \times 10^{-6}) \times v}=\frac{h}{(9.1 \times 10^{-31}) \times(3 \times 10^{6})} \\ & \Rightarrow v=\frac{9.1 \times 10^{-31} \times 3 \times 10^{6}}{10^{-6}}=2.73 \times 10^{-18} ms^{-1} \end{aligned} $