JEE Main 2019 — Structure Of Atom Question with Solution

(a) Angular momentum, $$mvr=\frac{nh}{2\pi }$$

$$\Rightarrow mvr\propto n$$ $$\propto$$ distance from the nucleus

(b) This statement is incorrect as size of an orbit $$\propto$$ Azimuthal quantum number (l) ($$\because$$ n = constant)

(c) This statement is incorrect as at ground state,

n = 1, l = 0

$$\Rightarrow$$ Orbital angular momentum (wave mechanics)

$$=\sqrt{l(l+1)}\frac{h}{2\pi }=0$$ [$$\because$$ $$l=0$$]

(d) The plot of $$\psi$$ vs $$r$$ for various azimuthal quantum numbers, shows peak shifting towards higher $$r$$ value.
This statement is typically true. The radial distribution functions of atomic orbitals (which can be related to $$|\psi {|}^2$$ vs $$r$$) for higher azimuthal quantum numbers generally have their peaks at larger values of the radial distance $$r$$ from the nucleus. This is because with higher $$l$$ values, the electrons are more likely to be found at greater distances due to the higher angular momentum.