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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

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