1

### AIPMT 2003

The velocity of Planck's constant is 6.63 $\times$ 10$-$34 J s.

The velocity of light is 3.0 $\times$ 108 m s$-$1. Which value is closest to the wavelength in nanometers of a quantum of light with frequency of 8 $\times$ 1015 s$-$1 ?
A
2 $\times$ 10$-$25
B
5 $\times$ 10$-$18
C
$4 \times {10^1}$
D
3 $\times$ 107

## Explanation

$v$ = c/$\lambda$

$\lambda$ = ${c \over v}$ = ${{3 \times {{10}^8}} \over {8 \times {{10}^{15}}}}$ = 37.5 $\times$ 10-9 m

= 37.5 nm $\approx$ $4 \times {10^1}$ nm
2

### AIPMT 2002

In hydrogen atom, energy of first excited state is $-$ 3.4 eV. Then find out K.E. of same orbit of hydrogen atom
A
+3.4 eV
B
+6.8 eV
C
$-$ 13.6 eV
D
+13.6 eV

## Explanation

K.E = 1/2 mv2

= ${\left( {{{\pi {e^2}} \over {nh}}} \right)^2} \times 2m$ [ $\because$ v = ${{2\pi {e^2}} \over {nh}}$]

$\therefore$ Total energy = En = ${{ - 2{\pi ^2}m{e^4}} \over {{n^2}{h^2}}}$

= -${\left( {{{\pi {e^2}} \over {nh}}} \right)^2}$ $\times$ 2m = -K.E

$\therefore$ K.E = - En

Energy of first excited state is -3.4 eV

$\therefore$ Kinetic energy of the same orbit (n = 2) will be +3.4 ev
3

### AIPMT 2001

The following quantum numbers are possible for how many orbitals :

n = 3, $l$ = 2, m = +2 ?
A
1
B
2
C
3
D
4

## Explanation

n = 3, l = 2, m = +2

It shows one of the five d-orbitals(3d)
4

### AIPMT 2001

Main axis of a diatomic molecule is z, molecular orbital px and py overlap to from which of the following orbitals.
A
$\pi$ molecular orbital
B
$\sigma$ molecular orbital
C
$\delta$ molecular orbital
D
No bond will form

## Explanation

For $\pi$ overlap, the lobes of the atomic orbitals are perpendicularto the line joining the nuclei.

Hence only sidewise overlapping takes place.