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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2010

MCQ (Single Correct Answer)
Ionisation energy of He+ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of Li2+ is
A
4.41 x 10–16 J atom–1
B
-4.41 x 10–17 J atom–1
C
-2.2 x 10–15 J atom–1
D
8.82 x 10–17 J atom–1

Explanation

Ionisation energy(IE) - It is the energy required to move an electron from ground state to infinity.

IE = $${E_\infty } - {E_1}$$ = $$0 - {E_1}$$ = $$ - {E_1}$$

$$\therefore$$ E1 of He+ = - 19.6 x 10–18 J atom–1

Energy of a species at n state,

(En)species = (En)hydrogen $$ \times $$ Z2

$$\therefore$$ (E1)hydrogen = $${{ - 19.6 \times {{10}^{ - 18}}} \over 4}$$ [ For He, Z = 2 ]

(E1)Li+2 = $${{ - 19.6 \times {{10}^{ - 18}}} \over 4} \times {3^2}$$

= -4.41 x 10–17 J atom–1
2

AIEEE 2010

MCQ (Single Correct Answer)
The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol–1. The longest wavelength of light capable of breaking a single Cl – Cl bond is
(c = 3 x 108 ms–1 and NA = 6.02 x 1023 mol–1)
A
594 nm
B
640 nm
C
700 nm
D
494 nm

Explanation

Energy required to break one Cl2 molecule = $${{242 \times {{10}^3}} \over {6.02 \times {{10}^{23}}}}$$ J

As E = $${{hc} \over \lambda }$$

So $$\lambda = {{hc} \over E}$$

= $${{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8} \times 6.02 \times {{10}^{23}}} \over {242 \times {{10}^3}}}$$

= 494 $$ \times $$ 10-9 m

= 494 nm
3

AIEEE 2009

MCQ (Single Correct Answer)
In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h = 6.6 $$\times$$ 10-34 kg m2s-1, mass of electron, em = 9.1 $$\times$$ 10-31 kg)
A
5.10 $$\times$$ 10-3 m
B
1.92 $$\times$$ 10-3 m
C
3.84 $$\times$$ 10-3 m
D
1.52 $$\times$$ 10-4 m

Explanation

% error in velocity = $${{\Delta V} \over V} \times 100$$

$$ \therefore $$ 0.005 = $${{\Delta V} \over {600}} \times 100$$

$$ \Rightarrow $$ $$\Delta $$V = 3 $$ \times $$ 10-2

According to Heisenberg uncertainty principle,

$$\Delta x.m\Delta V \ge {h \over {4\pi }}$$

$$ \Rightarrow $$ $$\Delta x = {h \over {4\pi m\Delta V}}$$

$$ \Rightarrow $$ $$\Delta x = {{6.63 \times {{10}^{ - 34}}} \over {4 \times 3.14 \times 9.1 \times {{10}^{ - 31}} \times 3 \times {{10}^{ - 2}}}}$$

             = 1.92 $$ \times $$ 10-3 m
4

AIEEE 2009

MCQ (Single Correct Answer)
Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 103 ms−1 (Mass of proton = 1.67 $$\times$$ 10-27 kg and h = 6.63 $$\times$$ 10-34 Js) :
A
0.40 nm
B
2.5 nm
C
14.0 nm
D
0.32 nm

Explanation

Wavelength$$\left( \lambda \right)$$ = $${h \over {mv}}$$

= $${{6.63 \times {{10}^{ - 34}}} \over {1.67 \times {{10}^{ - 27}} \times {{10}^3}}}$$

= 0.4 $$\times$$ 10-9

= 0.4 nm

Questions Asked from Structure of Atom

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