Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^{3} \mathrm{~ms}^{-1}$ (Mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$ and $\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}$ ) :

JEE Main · 2009 · 12 Apr 2009 · Offline · Atomic Structure

Calculate the wavelength (in nanometer) associated with a proton moving at

1.0 \times 1 0^{3} ms^{- 1}

(Mass of proton

= 1.67 \times 1 0^{- 27} kg

and

h = 6.63 \times 1 0^{- 34} Js

) :

Answer: (B)

The de Broglie wavelength of a moving particle is

λ = \frac{h}{m v}

. Substituting the proton values,

λ = \frac{6.63 \times 1 0 ^{- 34}}{1.67 \times 1 0 ^{- 27} \times 1.0 \times 1 0 ^{3}} \approx 3.97 \times 1 0^{- 10}

m, and expressing this in nanometres gives about 0.40 nm.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option