Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 × 10^3 m/s . (Mass of proton = 1.67 × 10^-27 kg and h = 6.63 × 10^-34 J - Chemistry MCQ AIEEE 2009 2026 | ExamTest.live

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1 mark

Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 \times 1 0^{3} m/s . (Mass of proton = 1.67 \times 1 0^{- 27} kg and h = 6.63 \times 1 0^{- 34} J s):

Solution & Step-by-step Explanation

Using the de Broglie wavelength formula: λ = \frac{h}{m v} Substituting the given values: λ = \frac{6.63 \times 1 0 ^{- 34} J s}{( 1.67 \times 1 0 ^{- 27} kg ) \times ( 1.0 \times 1 0 ^{3} m/s )} λ = \frac{6.63}{1.67} \times 1 0^{- 34 + 27 - 3} m λ \approx 3.97 \times 1 0^{- 10} m To convert to nanometers (1 nm = 1 0^{- 9} m): λ = 0.397 nm \approx 0.40 nm

Try it yourself before checking the explanation above.

Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 \times 1 0^{3} m/s . (Mass of proton = 1.67 \times 1 0^{- 27} kg and h = 6.63 \times 1 0^{- 34} J s):

0.032 nm

0.40 nm

2.5 nm

14.0 nm

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