According to Bohrs theory of hydrogen atom, the angular momentum of an electron in any orbit of hydrogen atom is:

Question

According to Bohrs theory of hydrogen atom, the angular momentum of an electron in any orbit of hydrogen atom is: (A) directly proportional to radius of orbit (B) inversely proportional to the radius of orbit (C) directly proportional to the square of the orbit radius (D) directly proportional to the square root of the radius of the orbit

Tardigrade Admin · Accepted Answer

From Bohrs theory of hydrogen atom electrons can revolve only in those orbits in which their angular momentum is an integral multiple of

\frac{h}{2 π}

L = n \frac{h}{2 π}

...(i)
Also, radius of

n^{t h}

orbit of atom is

r_{n} = n^{2} a_{0}

...(ii)
where

a_{0}

is Bohrs radius.
From Eqs. (i) and (ii), we get

L \propto r_{n}

Q. According to Bohrs theory of hydrogen atom, the angular momentum of an electron in any orbit of hydrogen atom is:

directly proportional to radius of orbit

inversely proportional to the radius of orbit

directly proportional to the square of the orbit radius

directly proportional to the square root of the radius of the orbit

From Bohrs theory of hydrogen atom electrons can revolve only in those orbits in which their angular momentum is an integral multiple of 2πh​ L=n2πh​ ...(i) Also, radius of nth orbit of atom is rn​=n2a0​ ...(ii) where a0​ is Bohrs radius. From Eqs. (i) and (ii), we get L∝rn​​