Test: Heisenberg's Uncertainty Principle - EmSAT Achieve MCQ

Given Δt = 2 × 10^-2 sec;
From the second equation,

Therefore, minimum uncertainty in energy is 
ΔE = 2.638 × 10^-33 J;
Converting in eV,
ΔE = (2.638 × 10^-33)/(1.6 × 10^-19) eV = 1.6 × 10^-14 eV;

• From the above, it is clear that, the particles that are indistinguishable and obey both Heisenberg's uncertainty principle and Pauli's exclusion principle are Fermi-Dirac statistics.

According to this law:

⇒ Range (R) = (m/3k) v³

Where m is mass, k is a constant and v is velocity.

The kinetic energy (E) is given by:

⇒ E = (1/2)m v²

The above equation can be written for v as,

⇒ v = (2E/m)^1/2

So the range is given by:

⇒ R = (m/3k) × (2E/m)^3/2 = (2^3/3 m^-1/2/3k) E^3/2

• From the above, it is clear that Geiger's law found the correlation between the decay constant (λ =0.693/T) and the alpha energies. Therefore option 3 is correct.

v = 300 m/s, Δv = 0.001 % of V;
⇒ Δv = 300 × 0.001 × 10^-2 = 3 × 10^-3 m/s;

Heisenberg’s uncertainty principle is a key principle in quantum mechanics.

Very roughly, it states that if we know everything about where a particle is located (the uncertainty of position is small), we know nothing about its momentum (the uncertainty of momentum is large), and vice versa.

Versions of the uncertainty principle also exist for other quantities as well, such as energy and time.

We discuss the momentum-position and energy-time uncertainty principles separately.

The Heisenberg Uncertainty Principle applies to electrons and protons as well, it is applicable for all small particles.

Heisenberg’s uncertainty principle is given by

Heisenberg's uncertainty principle talks about either position, momentum pair or energy, time pair.

• Pauli exclusion principle states that in a single atom no two electrons will have an identical set or the same quantum numbers i.e. every electron should have or be in its own unique state (singlet state).
• There are two salient rules that the Pauli Exclusion Principle follows:
  • Only two electrons can occupy the same orbital.
  • The two electrons that are present in the same orbital must have opposite spins or it should be antiparallel.
• However, Pauli Exclusion Principle does not only apply to electrons.
• It applies to other particles of half-integer spin such as fermions. It is not relevant for particles with an integer spin such as bosons which have symmetric wave functions.

Δvx = 4 × 10³ m/s, h = 6.63 × 10-34 J-s;
Mass of the proton = 1.67 × 10^-27 kg;
From the uncertainty principle,

∴ minimum uncertainity involved in measuring the position will be 7.9 × 10^-12 m.

Substituting E = hv in Heisenberg’s uncertainty principle for position and momentum gives an expression in terms of energy and time as another variable pair that appears in this uncertainty principle. Momentum and velocity, time and position, and energy and momentum are not complementary pairs in this regard.

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).

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°.