Dual Nature of Radiation and Matter - Result Question 14
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:
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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:
c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (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:
- (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} $
