Solved Practice Questions on Towards Quantum Mechanical Model of Atom | Physical Chemistry PDF Download

Q.1. A ball of mass 0.5kg is moving with velocity 6.626 m/s. What’s the wavelength of that ball?
(a) 1 x 10^-34 m
(b) 2 x 10^-34 m
(c) 2 x 10^-32 m
(d) 2 x 10^-3 m

Correct Answer is Option (b)
Louis de Brogie gave the realation between momentum and wavelength as λ = h/p. Here h is Planck’s constant, whose value is 6.626 x 10^-34 J/s. Wavelength = h/mv = 2 x 10^-34 m (momentum p = mass m x velocity v). 

Q.2. Determining the exact position and velocity of an electron is impossible at a time.
(a) True
(b) False

Correct Answer is Option (a)
A German physicist, Werner Heisenberg stated Heisenberg’s principle of uncertainty, that states that determining the exact position and velocity of an electron is impossible at a time, as a result of dual nature of matter and radiation. 

Q.3. The uncertainty of a ball is given by 0.5A°. Then calculate the uncertainty in momentum.
(a) 2.055 x 10^-24 kgm/s
(b) 1.015 x 10^-24 kgm/s
(c) 1.055 x 10^-24 kgm/s
(d) 1.095 x 10^-24 kgm/s

Correct Answer is Option (c)
Heisenberg’s principle of uncertainty states that Δx. Δp ≥ h/4π, x is position, p is momentum and “h” is the Planck’s constant and is equal to 6.626 x 10^-34 Js. Relative momentum Δp = h/4πΔx = 1.055 x 10^-24 kgm/s. 

Q.4. If the kinetic energy of an electron is 5J. Find out its wavelength.
(a) 0.313 x 10¹⁵ m/s
(b) 3.013 x 10¹⁵ m/s
(c) 3.310 x 10¹⁵ m/s
(d) 3.313 x 10¹⁵ m/s

Correct Answer is Option (d)
We know that the mass of an electron is 9.1 x 10^-31 kg. Given that the kinetic energy of an electron is 5J. K.E = mv²/2 and by substituting we get v = √1.098 x 10³¹ m/s = 3.313 x 10¹⁵m/s. 

Q.5. Δx. Δp ≥ h/4π.
(a) True
(b) False

Correct Answer is Option (a)
Heisenberg’s principle of uncertainty states that the product of relative momentum and velocities is equal to greater than the h/4π, where is “h” is the Planck’s constant and is equal to 6.626 x 10^-34 Js. Hence the above statement is true. 

Q.6. Who found out about dual behavior of a matter?
(a) De Broglie
(b) Bohr
(c) Rutherford
(d) Thomson

Correct Answer is Option (a)
A French physicist named Louis de Broglie proposed that matter exhibits both particle and wave like nature. This means that like photons, electrons also should have both momentum and wavelength. 

Q.7. Mass of a photon is given by 3.313 x 10^-34 kg. Find it’s wavelength.
(a) 0.67A°
(b) 0.67nm
(c) 0.37A°
(d) 1.67A°

Correct Answer is Option (a)
Louis de Brogie gave the realation between momentum and wavelength as λ = h/p. Here h is Planck’s constant, whose value is 6.626 x 10^-34 J/s. Wavelength = h/mc = 6.626 x 10^-34 Js/(3.313 x 10^-34 kg x 3 x 10⁸ m/s) = 0.67A°. 

Q.8. As per Heisenberg’s principle of uncertainty, the relation between relative momentum and relative position is _______
(a) independent
(b) equal
(c) directly proportional
(d) inversely proportional

Correct Answer is Option (d)
Heisenberg’s principle of uncertainty states that the product of relative momentum and velocities is equal to greater than the h/4π, where is “h” is the Planck’s constant and is equal to 6.626 x 10^-34 Js. 

Q.9. If the uncertainties in position and momentum are equal, then the uncertainty in position is given by _______
(a) √h/4π
(b) √h4π
(c) √h/4
(d) √h/π

Correct Answer is Option (a)
As we know, Heisenberg’s principle of uncertainty states that Δx. Δp ≥ h/4π, x is position, p is momentum and “h” is the Planck’s constant. Δx = Δp; Δx. Δx = h/4π; Δx = √h/4π 

Q.10. An object has a mass of 6 kg and velocity of 10 m/s. The speed is measured with 5% accuracy, then find out Δx in m.
(a) 0.12676 x 10^-34
(b) 0.1566 x 10^-34
(c) 0.176 x 10^-34
(d) 0.276 x 10^-34

Correct Answer is Option (c)
Speed’s uncertainty is 10 x 5/100 = 0.5 m/s. We have Heisenberg’s principle of uncertainty i.e. Δx. Δp ≥ h/4π. Δx = h/2mπ. Therefore uncertainty in position = 6.626 x 10^-34 Js/12 x 3.1416 = 0.176 x 10^-34.