Question

Match the column I with II and column II and mark the appropriate choice.

	Column I		Column II
(A)	Uncertainty of an object	(i)	$\frac{5.29\times n^2}{Z}$
(B)	Bohr's radius of an orbit	(ii)	$\frac{h}{4\pi m}$
(C)	Angular momentum of an electron	(iii)	$\frac{h}{mv}$
(D)	de Broglie wavelength	(iv)	$n.\frac{h}{2\pi }$

• A. $\left(A\right)\to \left(iii\right),\left(B\right)\to \left(iv\right),\left(C\right)\to \left(i\right),\left(D\right)\to \left(ii\right)$
• B. $\left(A\right)\to \left(ii\right),\left(B\right)\to \left(i\right),\left(C\right)\to \left(iv\right),\left(D\right)\to \left(iii\right)$
• C. $\left(A\right)\to \left(iv\right),\left(B\right)\to \left(iii\right),\left(C\right)\to \left(i\right),\left(D\right)\to \left(ii\right)$
• D. $\left(A\right)\to \left(i\right),\left(B\right)\to \left(ii\right),\left(C\right)\to \left(iv\right),\left(D\right)\to \left(iii\right)$

Answer 1

Answer: (B)

$\left(A\right)\to \left(ii\right),\left(B\right)\to \left(i\right),\left(C\right)\to \left(iv\right),\left(D\right)\to \left(iii\right)$

(A) Uncertainty of an object:

According to Heisenberg's uncertainity principle:

$\Delta x.\Delta p=\frac{h}{4\pi }$

$\Delta x.\Delta \left(mv\right)=\frac{h}{4\pi }$

$\Delta x.\Delta v=\frac{h}{4\pi m}$=(ii)

(B) Bohr's radius of an orbit, $r_n=\frac{5.29\times n^2}{Z}$=(i)

where, $n=n^{th}$ orbit, $Z$=atomic number

(C) Angular momentum of an electron is given by Bohr's theory as:

Thus an electron can move only in those orbits for which its angular momentum is integral multiple of $\frac{h}{2\pi }$ that is why only certain fixed orbits are allowed.

$mvr=\frac{nh}{2\pi }$=(iv)

(D) According to de Broglie's equation

$\lambda =\frac{h}{mv}$=(iii)

where, $\lambda =$ de-Broglie wavelength

(A)-(ii),(B)-(i),(C)-(iv),(D)-(iii)