# Iit Questions

Topics: Atom, Electron, Quantum mechanics Pages: 36 (7502 words) Published: June 17, 2012
Question 2.1:
(i) Calculate the number of electrons which will together weigh one gram. (ii) Calculate the mass and charge of one mole of electrons. * -------------------------------------------------
(i) Mass of one electron = 9.10939 × 10–31 kg
Number of electrons that weigh 9.10939 × 10–31 kg = 1
Number of electrons that will weigh 1 g = (1 × 10–3 kg)

= 0.1098 × 10–3 + 31
= 0.1098 × 1028
= 1.098 × 1027
(ii) Mass of one electron = 9.10939 × 10–31 kg
Mass of one mole of electron = (6.022 × 1023) × (9.10939 ×10–31 kg) = 5.48 × 10–7 kg
Charge on one electron = 1.6022 × 10–19 coulomb
Charge on one mole of electron = (1.6022 × 10–19 C) (6.022 × 1023) = 9.65 × 104 C
Question 2.2:
(i) Calculate the total number of electrons present in one mole of methane. (ii) Find (a) the total number and (b) the total mass of neutrons in 7 mg of 14C. (Assume that mass of a neutron = 1.675 × 10–27 kg).

(iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH3 at STP. Will the answer change if the temperature and pressure are changed? * -------------------------------------------------

(i) Number of electrons present in 1 molecule of methane (CH4) {1(6) + 4(1)} = 10
Number of electrons present in 1 mole i.e., 6.023 × 1023 molecules of methane = 6.022 × 1023 × 10 = 6.022 × 1024
(ii) (a) Number of atoms of 14C in 1 mole= 6.023 × 1023
Since 1 atom of 14C contains (14 – 6) i.e., 8 neutrons, the number of neutrons in 14 g of 14C is (6.023 × 1023) ×8. Or, 14 g of 14C contains (6.022 × 1023 × 8) neutrons. Number of neutrons in 7 mg

= 2.4092 × 1021
(b) Mass of one neutron = 1.67493 × 10–27 kg
Mass of total neutrons in 7 g of 14C
= (2.4092 × 1021) (1.67493 × 10–27 kg)
= 4.0352 × 10–6 kg
(iii) (a) 1 mole of NH3 = {1(14) + 3(1)} g of NH3
= 17 g of NH3
= 6.022× 1023 molecules of NH3
Total number of protons present in 1 molecule of NH3
= {1(7) + 3(1)}
= 10
Number of protons in 6.023 × 1023 molecules of NH3
= (6.023 × 1023) (10)
= 6.023 × 1024
⇒ 17 g of NH3 contains (6.023 × 1024) protons.
Number of protons in 34 mg of NH3

= 1.2046 × 1022
(b) Mass of one proton = 1.67493 × 10–27 kg
Total mass of protons in 34 mg of NH3
= (1.67493 × 10–27 kg) (1.2046 × 1022)
= 2.0176 × 10–5 kg
The number of protons, electrons, and neutrons in an atom is independent of temperature and pressure conditions. Hence, the obtained values will remain unchanged if the temperature and pressure is changed. Question 2.3:

How many neutrons and protons are there in the following nuclei? , , , ,
* -------------------------------------------------
136C:
Atomic mass = 13
Atomic number = Number of protons = 6
Number of neutrons = (Atomic mass) – (Atomic number)
= 13 – 6 = 7
:
Atomic mass = 16
Atomic number = 8
Number of protons = 8
Number of neutrons = (Atomic mass) – (Atomic number)
= 16 – 8 = 8
:
Atomic mass = 24
Atomic number = Number of protons = 12
Number of neutrons = (Atomic mass) – (Atomic number)
= 24 – 12 = 12
:
Atomic mass = 56
Atomic number = Number of protons = 26
Number of neutrons = (Atomic mass) – (Atomic number)
= 56 – 26 = 30
:
Atomic mass = 88
Atomic number = Number of protons = 38
Number of neutrons = (Atomic mass) – (Atomic number)
= 88 – 38 = 50
Question 2.4:
Write the complete symbol for the atom with the given atomic number (Z) and Atomic mass (A) (i) Z = 17, A = 35
(ii) Z = 92, A = 233
(iii) Z = 4, A = 9
* -------------------------------------------------
(i) (ii) (iii)
Question 2.5:
Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wave number () of the yellow light. * -------------------------------------------------
From the expression,

We get,
…….. (i)
Where,
ν = frequency of yellow light
c = velocity of light in vacuum = 3 × 108 m/s
λ = wavelength of yellow light = 580 nm = 580 × 10–9 m Substituting the values in expression (i):

Thus,...