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1

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

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

### AIPMT 2008

The measurement of the electron position is associated with an uncertainty in momentum, which is equal to 1 $$\times$$ 10$$-$$18 g cm s$$-$$1. The uncertainty in electron velocity is (mass of an electron is 9 $$\times$$ 10$$-$$28 g)
A
1 $$\times$$ 105 cm s$$-$$1
B
1 $$\times$$ 1011 cm s$$-$$1
C
1 $$\times$$ 109 cm s$$-$$1
D
1 $$\times$$ 106 cm s$$-$$1

## Explanation

$$\Delta v$$ = $${{1 \times {{10}^{ - 18}}} \over {9 \times {{10}^{ - 28}}}} = 1.1 \times {10^9}cm\,{s^{ - 1}}$$
3

### AIPMT 2007

Consider the following sets of quantum numbers :

n l m s
(i) 3 0 0 +1/2
(ii) 2 2 1 +1/2
(iii) 4 3 -2 -1/2
(iv) 1 0 -1 -1/2
(v) 3 2 3 +1/2

Which of the following sets of quantum number is not possible ?
A
(i), (ii), (iii) and (iv)
B
(ii), (iv) and (v)
C
(i) and (iii)
D
(ii), (iii) and (iv)

## Explanation

(i) represents an electron in 3s orbital

(ii) is not possible as value of m varies from 0, 1, .... ($$n$$ -1)

(iii) represents an electron in 4f orbital

(iv) is not possible as value of m varies from -$$l$$ ... +$$l$$

(v) is not possible as value of m varies from -$$l$$ ... +$$l$$, it can never be grater than $$l$$
4

### AIPMT 2006

Given : The mass of electron is 9.11 $$\times$$ 10$$-$$31 kg, Planck constant is 6.626 $$\times$$ 10$$-$$34 J s, the uncertainty involved in the measurement of velocity within a distance of 0.1 $$\mathop A\limits^ \circ$$ is
A
5.79 $$\times$$ 105 m s$$-$$1
B
5.79 $$\times$$ 106 m s$$-$$1
C
5.79 $$\times$$ 107 m s$$-$$1
D
5.79 $$\times$$ 108 m s$$-$$1

## Explanation

$$\Delta x.m\Delta v = h/4\pi$$

0.1 $$\times$$ 10-10 $$\times$$ 9.11 $$\times$$ 10-31 $$\times$$ $$\Delta v$$ = $${{6.626 \times {{10}^{ - 34}}} \over {4 \times 3.143}}$$

$$\therefore$$ $$\Delta v$$ = $${{6.626 \times {{10}^{ - 34}}} \over {4 \times 3.143 \times 0.1 \times {{10}^{ - 10}} \times 9.11 \times {{10}^{ - 31}}}}$$

= 5.79 $$\times$$ 106 m s-1

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