Atoms & Nuclei

JEE Main level, single correct, medium

88 of 239

Question 88 of 239

Which of the plots shown in the figure represents speed (v)(v) of the electron in a hydrogen atom as a function of the principal quantum number (n)(n) ?

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Answer: (A) BB

Velocity of electron in nth n^{\text {th }} orbit of hydrogen atom is given by :
Vn=2πKZe2nhV_n=\frac{2 \pi K Z e^2}{n h}
Substituting the values we get,
Vn=2.2×106n m/s or Vn∝1nV_n=\frac{2.2 \times 10^6}{n} \mathrm{~m} / \mathrm{s} \quad \text { or } \quad V_n \propto \frac{1}{n}
As principal quantum number increases, velocity decreases.

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