Competishun Header

Report Issue

JEE Advanced 2016
Paper-1 2016
Multiple correct answers - Select all that apply
Question
Highly excited states for hydrogen-like atoms (also called Rydberg states) with nucles charge Ze are defined by their principal quantum number n, where n>>1. Which of the following statement(s) is(are) true?
Select ALL correct options:
A
Relative change in the radii of two consecutive orbitals does not depend on Z.
B
Relative change in the radii of two consecutive orbitals varies as 1/n.
C
Relative change in the energy of two consecutive orbitals varies as $1 / n^3$.
D
Relative change in the angular momenta of two consecutive orbitals varies as 1/n.
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
Solution
orbital :
$ \begin{aligned} & \& \quad \frac{\Delta r}{r}=\text { relative change } \\ & \begin{aligned} r_n= & 0.529 \frac{n^2}{Z} \\ = & \frac{(n+1)^2-n^2}{n^2} \\ = & \frac{n^2+1+2 n-n^2}{n^2} \\ = & \frac{1}{\infty}+\frac{2 n}{n^2} \\ = & \frac{1}{n} \quad \therefore \text { dependent on } n . \\ E_n=-13.6 \frac{z^2}{n^2} \quad & \text { Relative change }=\frac{\Delta E}{E} \end{aligned} \end{aligned} $
$\begin{aligned} & =\frac{\frac{1}{(n+1)^2}-\frac{1}{n^2}}{\frac{1}{n^2}} \\ & =\frac{n^2-n^2-1-2 n}{n^2(n+1)^2} \times \frac{n^2}{1} \\ \Rightarrow \quad & \frac{-(1+2 n)}{(n+1)^2}\end{aligned}$
$\begin{aligned} & \Rightarrow \quad \frac{1+2 n}{n^2+1+2 n} \\ & =\frac{1}{n^2+1+2 n}+\frac{2 n}{n^2+1+2 n} \\ & \text { Doesn't match with 'C' } \\ & L_n=\frac{n h}{2 \pi} \\ & \text { Relative change }=\frac{\Delta L}{L}=\frac{n-(n-1)}{n}=\frac{1}{n}\end{aligned}$
Question Tags
JEE Advance
Physics
Easy
Start Preparing for JEE with Competishun
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE-Main 20242024
The number of moles of methane required to produce $11 \mathrm{~g} \mathrm{CO}_2(\mathrm{~g})$ after complete combustion is: (Given molar mass of...
JEE MainChemistryEasy
View Solution
QJEE Main 20242024
Let the set of all values of $p$, for which $f(x)=\left(p^2-6 p+8\right)\left(\sin ^2 2 x-\cos ^2 2 x\right)+2(2-p) x+7$ does...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8 x$. If the set of all values of $\alpha$, for...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Let $\vec{a}=2 \hat{\imath}+\alpha \hat{\jmath}+\hat{k}, \dot{b}=-\hat{\imath}+\hat{k}, \vec{c}=\beta \hat{\jmath}-\hat{k}$, where $\alpha$ and $\beta$ are integers and $\alpha \beta=-6$. Let the values of...
JEE AdvanceMathematicsEasy
View Solution
QJEE Main 20242024
Let $\alpha, \beta ; \alpha>\beta$, be the roots of the equation $x^2-\sqrt{2} x-\sqrt{3}=0$. Let $P_n=\alpha^n-\beta^n, n \in N$. Then $...
JEE MainMathematicsEasy
View Solution
QJEE-Main 20242024
For the electro chemical cell
JEE MainChemistryEasy
View Solution
QJEE-Main 20242024
Consider the given chemical reaction :
JEE MainChemistryEasy
View Solution
QJEE-Main 20242024
consider-the-above-reaction-sequence-and-identify-the-major-product-p
JEE MainChemistryEasy
View Solution
QJEE-Main 20242024
Given below are two statements :
JEE MainChemistryEasy
View Solution
QJEE-Main 20242024
Which one of the following reactions is NOT possible?
JEE MainChemistryEasy
View Solution
QJEE-Main 20242024
The quantity of silver deposited when one coulomb charge is passed through $\mathrm{AgNO}_3$ solution:
JEE MainChemistryEasy
View Solution
QJEE Main 20242024
The sum of the coefficient of $x^{2 / 3}$ and $x^{-2 / 5}$ in the binomial expansion of $...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
The value of the integral $\int_{-1}^2 \log _e\left(x+\sqrt{x^2+1}\right) d x$ is :
JEE MainMathematicsEasy
View Solution
QJEE-Main 20242024
Match List - I with List - II.
JEE MainChemistryEasy
View Solution
QJEE Main 20242024
If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$...
JEE MainMathematicsEasy
View Solution
QJEE Main 20242024
Let a, ar, $a r^{2^2} \ldots \ldots .$. be an infinite G.P. If $\sum_{n=0}^{\infty} a^n=57$ and $\sum_{n=0}^{\infty} a^3 r^{3 n}=9747$,...
JEE MainMathematicsEasy
View Solution
QJEE-Main 20242024
The metal atom present in the complex MABXL (where $\mathrm{A}, \mathrm{B}, \mathrm{X}$ and L are unidentate ligands and M is...
JEE MainChemistryEasy
View Solution
QJEE Main 20242024
The integral $\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right) \mathrm{dx}$ is equal to:
JEE MainMathematicsEasy
View Solution
Check this project | Best Developer Portfolio