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GATE 2021 CY – Question 57

Physical Chemistry · Structure: Postulates of quantum mechanics. Operators. Commutation relations and expectations values; the role of the wave function and its absolute squares, time dependent and time independent Schrödinger equations. Born interpretation. Dirac bra-ket notation. Examples of model solvable quantum mechanical systems. · 2 marks · Numerical answer

An argon atom (40 amu) travels at 250 m/s. Its de Broglie wavelength is ______ pm (one decimal place). $N_A=6.022\times10^{23}$; $h=6.626\times10^{-34}$ kg m$^2$ s$^{-1}$.

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Correct answer: 39.5 to 40.5

Explanation

Convert the atomic mass to kilograms: m=(40×10⁻³)/(6.022×10²³)=6.6423×10⁻²⁶ kg. Then λ=h/(mv)=6.626×10⁻³⁴/(6.6423×10⁻²⁶×250)=3.9902×10⁻¹¹ m. Multiplying by 10¹² gives **39.9 pm** to one decimal.