1
MCQ (Single Correct Answer)

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
MCQ (Single Correct Answer)

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
MCQ (Single Correct Answer)

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
MCQ (Single Correct Answer)

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

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

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