JEE Advanced 2016 · Paper 1 · Physics Q6

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PhysicsMultiple correct+4 / -2Question 6 of 54

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge $Ze$ are defined by their principal quantum number $n$ , where $n\gg1$ . Which of the following statement(s) is(are) true?

Relative change in the radii of two consecutive orbitals does not depend on

Z

Relative change in the radii of two consecutive orbitals varies as

1/n

Relative change in the energy of two consecutive orbitals varies as

1/n^3

Relative change in the angular momenta of two consecutive orbitals varies as

1/n

Answer and worked solution

Official answer: A, B, D

For hydrogen-like atoms, $r_n\propto n^2/Z$ , $E_n\propto Z^2/n^2$ and $L_n=n\hbar$ .

Radii: $\dfrac{\Delta r}r=\dfrac{(n+1)^2-n^2}{n^2}\approx\dfrac2n$ . This does not depend on $Z$ and varies as $1/n$ . (A) and (B) are true.
Energy: $\dfrac{\Delta E}E\approx\dfrac2n$ , not $1/n^3$ . (C) is false.
Angular momentum: $\dfrac{\Delta L}L=\dfrac1n$ . (D) is true.

(A), (B), (D)

Topics:Bohr model and hydrogen spectrum

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JEE Advanced 2016 · Paper 1, Physics question 6