JEE Main 2019 — Structure Of Atom Question with Solution

Probablity density = $${\psi }^2$$
From the graph you can see probablity density is maximum at the nucleus where r = 0.

$$\therefore$$ Option A is correct.

(B) For hydrogen atom, electron can be found at a any distance distance from the nucleus.

$$\therefore$$ Option B is correct.

(C) Distance a₀ from the nucleus = First orbital

$$\therefore$$ n = 1 at first orbital

As Total energy, E_n = -13.6 $$\times$$ $$\frac{Z^2}{n^2}$$ eV

$$\therefore$$ Total energy for hydrogen at n = 1 is,

E₁ = -13.6 $$\times$$$$\frac{1^2}{1^2}$$ eV = -13.6 eV

So total energy is minimum at distance a₀ from the nucleus.

$$\therefore$$ Option C is incorrect.

(D) Total energy, E_n = -13.6 $$\times$$ $$\frac{Z^2}{n^2}$$ eV

Kinetic energy, K.E = 13.6 $$\times$$ $$\frac{Z^2}{n^2}$$ eV

Potential energy, P.E = -27.2 $$\times$$ $$\frac{Z^2}{n^2}$$ eV

$$\therefore$$ Magnitude of potential energy is double that of its kinetic energy.

$$\therefore$$ Option D is correct.