First slide

Wave nature of matter

Question

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is $1.878 \times 10^{- 4}$ . The mass of the particle is close to:

Moderate

A

$4.8 \times 10^{- 27} k g$
B

$1.2 \times 10^{- 28} k g$
C

$9.1 \times 10^{- 31} k g$
D

$9.7 \times 10^{- 28} k g$

Solution

$\begin{array}{l} λ_{P} = \frac{h}{M_{P} V_{P}}; λ_{e} = \frac{h}{M_{e} V_{e}} \\ \Rightarrow \frac{λ_{P}}{λ_{e}} = \frac{M_{e} V_{e}}{M_{P} V_{P}} \\ G i v e n V_{P} = 5 V_{e} \\ \Rightarrow 1.878 \times 10^{- 4} = \frac{M_{e}}{M_{P}} \frac{1}{5} \\ \Rightarrow M_{P} = \frac{9.1 \times 10^{- 31}}{5 \times 1.878 \times 10^{- 4}} = 9.69 \times 10^{- 28} k g ≅ 9.7 \times 10^{- 28} k g \end{array}$

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