JEE Advanced · 2016 · 22 May 2016 · Paper 1 · Atomic Structure

P

is the probability of finding the

1 s

electron of hydrogen atom in a spherical shell of infinitesimal thickness,

d r

, at a distance

r

from the nucleus. The volume of this shell is

4 π r^{2} d r

. The qualitative sketch of the dependence of

P

r

Answer: (D)

Solution

The probability

P

of finding the

1 s

electron in a spherical shell of thickness

d r

at distance

r

is given by the radial distribution function

P (r) = 4 π r^{2} ∣ ψ_{1 s} ∣^{2}

. For the hydrogen

1 s

orbital,

ψ_{1 s} \propto e^{- r / a_{0}}

, so

P (r) \propto r^{2} e^{- 2 r / a_{0}}

. This function starts at zero (when

r = 0

), rises to a maximum at

r = a_{0}

(the Bohr radius), and then decays exponentially to zero as

r \to \infty

. Option (D) shows this characteristic shape with a single maximum.

JEE Advanced · 2016 · 22 May 2016 · Paper 1 · Single correct option