JEE Advanced · Chemistry · 2. Atomic Structure

Statement 1 The plot of atomic number ( \(Y\)-axis) versus number of neutrons ( \(x\)-axis) for stable nuclei shows a curvature towards \(X\)-axis from the line of \(45^{\circ}\) slope as the atomic number is increased.
Statement 2 Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.

A Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
B Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
C Statement 1 is true, Statement 2 is false.
D Statement 1 is false, Statement 2 is true

Verified Solution

Answer & Solution

Correct Answer

(A) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

Step-by-step Solution

Detailed explanation

The stability relationship can be represented by a line with a slope of \(45^{\circ}\), i.e. the maximum stability is attained, when \(N=Z\).
Right or the curve a radioactive nuclide would be neutron rich and would decay be \(\beta\)-emission to produce a daughter nucleus with a lower \(\frac{n}{p}\) ratio.
For heavier nuclides, \(p-p\) repulsions start to offset the attractive forces and an excess of neutrons over protons, is required for stability

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

On complete hydrogenation, natural rubber produces

JEE Advanced 2016 Easy

The wave function,

ψ_{n, l, m_{l}}

is a mathematical function whose value depends upon spherical polar coordinates

(r, θ, ϕ)

of the electron and characterized by the quantum numbers

n, l

and

m_{l}

. Here

r

is the distance from the nucleus,

θ

is colatitude and

ϕ

is azimuth. In the mathematical functions given in the Table,

Z

is the atomic number and

a_{o}

is Bohr radius

Column 1	Column 2	Column 3
(I) 1s orbital	\(\text {(i) } \psi_{ n , 1, m_1}\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{3}{2}} e ^{-\left(\frac{ Zr }{ e _{ o }}\right)}\)	(P)
(II) 2s orbital	(ii) One radial node	(Q) Probability density at the nucleus \(\propto \frac{1}{ a _{ o }^3}\).
(III) \(2 p _{ z }\) orbital	\(\text {(iii) } \psi_{ n }, 1, m_{ l }\) \(\propto\left(\frac{ Z }{ a _{ o }}\right)^{\frac{5}{2}} re ^{-\left(\frac{ Zr }{2 a _{ o }}\right)} \cos \theta\)	(R) Probability density is maximum at the nucleus.
(IV) \(3 d_{ z }^2\) orbital	(iv) \(x y\)-plane is a nodal plane	(S) Energy needed to excite an electron from \(n =2\) state to \(n =4\) state is \(\frac{27}{32}\) times the energy needed to excite are electron from \(n =2\) state to \(n =6\) state.

For hydrogen atom, what is the only CORRECT combination?

JEE Advanced 2017 Hard

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