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Answer the following by appropriately matching the lists based on the information given in the paragraph.
Consider the Bohr's model of a one -electron atom where the electron moves around the nucleus. In the following $$List-I$$ contains some quantities for the $$n^{th}$$ orbit of the atom and $$List-II$$ contains options showing how they depend in $$n$$.

List-I
List-II
(i)Radius of the $$n^{th}$$ orbit(P)$$\propto n^{-2}$$
(ii)Angular momentum of the electron in the $$n^{th}$$ orbit(Q)$$\propto
n^{-1}$$
(iii)Kinetic energy of the electron in the $$n^{th}$$ orbit(R)$$\propto n^{0}$$
(IV)Potential energy of the electron in the $$n^{th}$$(S)$$\propto n^{1}$$
(T)$$\propto n^{2}$$
(U)$$\propto n^{\frac{1}{2}}$$

Which of the following has the correct combination considering $$List-I$$ and $$List-II$$?

A
$$(II),(R)$$
B
$$(II),(Q)$$
C
$$(I),(T)$$
D
$$(I),(P)$$
Solution
Verified by Toppr

Correct option is D. $$(I),(T)$$
The kinetic energy of the electron in the $$n^{th}$$ orbit is given as:
$$K.E.=\dfrac{me^4}{8{{\epsilon}_0}^2n^2h^2}$$
$$\therefore \ K.E.\propto n^{-2}$$
Similarly,
radius of $$n^{th}$$ orbit $$r\propto \dfrac{n^2}{Z}$$
Angular momentum $$|L|\propto n$$
and Potential energy $$P.E. \propto \dfrac {-Z^2}{n^2}$$

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