Towards Quantum Mechanical Model of the Atom - Dual Behaviour of Matter: De Broglie's relationship

The velocity associated with a proton moving in a potential difference of 1000 V is 4.37 × 10⁵ ms^–1. If the hockey ball of mass 0.1 kg is moving with this velocity, calculate the wavelength associated with this velocity.

According to de Broglie, matter should exhibit dual behaviour, that is both particle and wave like properties. However, a cricket ball of mass 100 g does not move like a wave when it is thrown by a bowler at a speed of 100 km/h. Calculate the wavelength of the ball and explain why it does not show wave nature.

The de Broglie's wavelength of electron emitted by metal will be ______ Å whose threshold frequency is 2.25 × 10¹⁴ Hz when exposed to visible radiation of wavelength 500 nm.

Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is 1.6 × 10⁶ ms^–1, calculate de Broglie wavelength associated with this electron.

Assertion (A): All isotopes of a given element show the same type of chemical behaviour.

Reason (R): The chemical properties of an atom are controlled by the number of electrons in the atom.

The mass of an electron is 9.1 × 10^–31 kg. If its K.E. is 3.0 × 10^–25 J, calculate its wavelength.

The de Broglie wavelength of an electron in the 4^th Bohr orbit is ______.

Calculate the wavelength of an electron moving with a velocity of 2.05 × 10⁷ ms^-1.