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← JEE Main 2021 · 24 Feb · Shift 1
ChemistryInteger+4 / -1Question 53 of 90

JEE Main 2021 · 24 Feb · Shift 1, Chemistry question 53

A proton and a Li3+^{3+} nucleus are accelerated by the same potential. If λLi_{Li} and λp_p denote the de Broglie wavelengths of Li3+^{3+} and proton respectively, then the value of λLiλp\dfrac{\lambda_{Li}}{\lambda_p} is x×10−1x\times10^{-1}. The value of xx is _______. (Rounded off to the nearest integer)

[Mass of Li3+^{3+} = 8.3 mass of proton]

Answer and worked solution

Official answer: 2

Same potential. λ=h2mqV\lambda=\frac h{\sqrt{2mqV}}, so λLiλp=18.3×3≈0.2=2×10−1\frac{\lambda_{Li}}{\lambda_p}=\sqrt{\frac1{8.3\times3}}\approx0.2=2\times10^{-1}.

Answer: 2