CBSE Class 12 Physics 2015 Delhi Set 1 Paper

Question : 7 of 26

Marks: +1, -0

Show that the radius of the orbit in hydrogen atom varies as

n^2

, where

n

is the principal quantum number of the atom.

Solution:

Showing that the radius of orbit varies as

n^2

\;\; \frac{m v^2}{r} = \; \frac{1}{4 \pi \varepsilon_0} \; \frac{e^2}{r^2}

\; m v^2 r = \; \frac{1}{4 \pi \varepsilon_0} e^2

.......(i)

m v r = \frac{n h}{2 \pi}

m^2 v^2 r^2 = \frac{n^2 h^2}{4 \pi^2}

.......(ii)

Divide (ii) by (i)

\; m r \; = \; \frac{n^2 h^2}{4 \pi^2} \times \frac{4 \pi \varepsilon_0}{e^2}

\therefore \; r \; = \; \frac{n^2 h^2}{4 \pi^2 m e^2} \cdot 4 \pi \varepsilon_0

\therefore \; r \propto n^2

(Give full credit to any other correct alternative method)

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