Question

For an atom having atomic number $z$.
Match the following:
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) Radius of orbit}& \text{(p) is proportional to z}\\ \text{(B) Current associated due to orbital motion of electron}& \text{(q) is inversely proportional to z}\\ \text{(C) Magnetic field at the centre due to orbital motion of electron}& {\text{(r) is proportional to z}}^2\\ \text{(D) Velocity of an electron}& {\text{(s) is proportional to z}}^3\end{array}$

• A. A – q, B – p, C – r, D – s
• B. A – q, B – r, C – s, D – p
• C. A – p, B – r, C – q, D – s
• D. A – s, B – p, C – r, D – q

Answer 1

The correct option is B A – q, B – r, C – s, D – p

A) $r\propto \frac{n^2}{z}$
B) $i=\frac{qv}{2\pi r}\text{and}v\propto \frac{z}{n}\Rightarrow i\propto \left(\frac{z}{n}\right)\left(\frac{z}{n^2}\right)$
$\Rightarrow i\propto z^2$
C) $B=\frac{{\mu }_{0}i}{2r}\Rightarrow B\propto \left(\frac{z^2}{n^3}\right)\left(\frac{z}{n^2}\right)$
$\Rightarrow B\propto z^3$
d) $v\propto \frac{z}{n}$