Magnetic field at the centre (at Nucleus) of the hydrogen like atoms (atomic No. Z) due to motion of electron in nt h orbit is proportional to

Question

Magnetic field at the centre (at Nucleus) of the hydrogen like atoms (atomic No. Z) due to motion of electron in nt h orbit is proportional to (A) (n3/Z5) (B) (n4/Z) (C) (Z2/n3) (D) (Z3/n5)

Tardigrade Admin · Accepted Answer

Bn=(μ 0 In/2 rn) or Bn propto (In/rn) propto (fn/rn) propto (vn/rn2) ⇒ Bn propto (z / n/(n2 / z)2) propto (z3/n5)

Q. Magnetic field at the centre (at Nucleus) of the hydrogen like atoms (atomic No. Z) due to motion of electron in $n^{t h}$ orbit is proportional to

$\frac{n ^{3}}{Z ^{5}}$

$\frac{n ^{4}}{Z}$

$\frac{Z ^{2}}{n ^{3}}$

$\frac{Z ^{3}}{n ^{5}}$

$B_{n} = \frac{μ _{0} I _{n}}{2 r _{n}}$
or $B_{n} \propto \frac{I _{n}}{r _{n}} \propto \frac{f _{n}}{r _{n}} \propto \frac{v _{n}}{r _{n}^{2}}$
$\Rightarrow B_{n} \propto \frac{z / n}{( n ^{2} / z ) ^{2}} \propto \frac{z ^{3}}{n ^{5}}$

Q. Magnetic field at the centre (at Nucleus) of the hydrogen like atoms (atomic No. Z) due to motion of electron in nth orbit is proportional to

Z5n3​

Zn4​

n3Z2​

n5Z3​