Towards Quantum Mechanical Model of the Atom - Heisenberg’s Uncertainty Principle

Match the following rules with their statements :

The quantum mechanical treatment of the hydrogen atom gives the energy value:

E_n = `(-13.6)/"n"^2` ev atom⁻¹

1. use this expression to find ΔE between n = 3 and n = 4
2. Calculate the wavelength corresponding to the above transition.

If the position of the electron is measured within an accuracy of ± 0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is h/4π_m × 0.05 nm, is there any problem in defining this value.

Which of the following is responsible to rule out the existence of definite paths or trajectories of electrons?

The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particles. Justify the statement with the help of a suitable example.

Table-tennis ball has a mass 10 g and a speed of 90 m/s. If speed can be measured within an accuracy of 4% what will be the uncertainty in speed and position?

In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainty with which the position of the electron can be located is ______.

(h = 6.6 × 10⁻³⁴ kg m²s⁻¹, mass of electron, e_m = 9.1 × 10⁻³¹ kg)

Which of the following does not represent the mathematical expression for the Heisenberg uncertainty principle?