1

### 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, $\lambda$ = ${h \over {mv}}$

$\therefore$ $\lambda$ = ${{6.6 \times {{10}^{ - 34}}} \over {0.66 \times 100}} = 1 \times {10^{ - 35}}\,m$
2

### 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
3

### AIPMT 2009

Maximum number of electrons in a subshell of an atom is determined by the following
A
2$l$ + 1
B
4$l$ $-$ 2
C
2n2
D
4$l$ + 2

## Explanation

Maximum number of electrons in a subshell = 2(2l+1) = 4l + 2
4

### AIPMT 2008

If uncertainty in position and momentum are equal, then uncertainty in velocity is
A
${1 \over m}\sqrt {{h \over \pi }}$
B
$\sqrt {{h \over \pi }}$
C
${1 \over {2m}}\sqrt {{h \over \pi }}$
D
$\sqrt {{h \over {2\pi }}}$

## Explanation

According to Heisenberg uncertainty principle

$\Delta p.\Delta x \ge {h \over {4\pi }}$ or m$\Delta v.\Delta x \ge {h \over {4\pi }}$

$\Rightarrow$ (m$\Delta v$)2 $\ge {h \over {4\pi }}$ ($\because$ $\Delta x$ = $\Delta p$)

$\Rightarrow$ $\Delta v \ge$ ${1 \over {2m}}\sqrt {{h \over \pi }}$