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IIT JEE Advanced 2010 Paper 2

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The hydrogen-like species

Li^{2+}

is in a spherically symmetric state

S_1

with one radial node. Upon absorbing light, the ion undergoes transition to a state

S_2

. The state

S_2

has radial node and its energy is equal to the ground state energy of the hydrogen atom.

Section: Chemistry

Question : 34 of 57

Marks: +1, -0

The state

S_1

Solution:

For

S_1

(spherically symmetrical), number of radial node = 1.

Therefore, n - l - 1 = 1.

⇒ n = 2 (as l = 0 for spherically symmetrical s orbital)

For

S_2

state, we have

E_{S2}

= - 13.6 ×

\frac{Z^2}{n^2}

Also, given that

E_H

in ground state = –13.6

Therefore,

E_{S2}

= - 13.6 ×

\frac{9}{n^2}

= - 13.6 ⇒ n = 3

Since the number of radial node = 1, substituting in n - l - 1 = 1, we get l = 1.

So, the state is

S_1

is 2s and

S_2

is 3p.

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