1

### AIPMT 2011 Prelims

The energies E1 and E2 of two radiations are 25 eV and 50 eV respectively. The relation between their wavelengths i.e., $\lambda$1 and $\lambda$2 will be
A
$\lambda$1 = $\lambda$2
B
$\lambda$1 = 2$\lambda$2
C
$\lambda$1 = 4$\lambda$2
D
$\lambda$1 = ${1 \over 2}$ $\lambda$2

## Explanation

E1 = ${{hc} \over {{\lambda _1}}}$ and E2 = ${{hc} \over {{\lambda _2}}}$

${{{E_1}} \over {{E_2}}}$ = ${{hc} \over {{\lambda _1}}} \times {{{\lambda _2}} \over {hc}}$ = ${{{\lambda _2}} \over {{\lambda _1}}}$

$\Rightarrow$ $25 \over 50$ = ${{{\lambda _2}} \over {{\lambda _1}}}$

$\Rightarrow$ $1 \over 2$ = ${{{\lambda _2}} \over {{\lambda _1}}}$ $\Rightarrow$ $\lambda _1$ = 2$\lambda _2$
2

### AIPMT 2011 Prelims

The total number of atomic orbitals in fourth energy level of an atom is
A
8
B
16
C
32
D
4

## Explanation

The total number of atomic orbitals in any energy level is n2.

$\therefore$ 42 = 16
3

### AIPMT 2010 Mains

A 0.66 kg ball is moving with a speed of 100 m/s. The associated wavelength will be

(h = 6.6 $\times$ 10$-$34 J s)
A
6.6 $\times$ 10$-$32 m
B
6.6 $\times$ 10$-$34 m
C
1.0 $\times$ 10$-$35 m
D
1.0 $\times$ 10$-$32 m

## Explanation

According to the de-Broglie equation, $\lambda$ = ${h \over {mv}}$

$\therefore$ $\lambda$ = ${{6.6 \times {{10}^{ - 34}}} \over {0.66 \times 100}} = 1 \times {10^{ - 35}}\,m$
4

### AIPMT 2009

Which of the following is not permissible arrangement of electrons in an atom ?
A
n = 5, $l$ = 3, m = 0, s = +1/2
B
n = 3, $l$ = 2, m = $-$ 3, s = $-$1/2
C
n = 3, $l$ = 2, m = $-$ 2, s = $-$1/2
D
n = 4, $l$ = 0, m = 0, s = $-$1/2

## Explanation

In an atom for any value of n, the values of l = 0 to (n-1)

For a given value of l, the values of ml = -$l$ to 0 to +$l$

and the value of s = +1/2 or -1/2

In option(b), l = 2 and ml = -3

This is not possible. as for l = 2 min value of ml = -2