Wave Nature of Matter

Two particles A₁ sand A₂ of masses m₁, m₂ (m₁ > m₂) have the same de Broglie wavelength. Then ______.

1. their momenta are the same.
2. their energies are the same.
3. energy of A₁ is less than the energy of A₂.
4. energy of A₁ is more than the energy of A₂.

An electromagnetic wave of wavelength ‘λ’ is incident on a photosensitive surface of negligible work function. If ‘m’ mass is of photoelectron emitted from the surface has de-Broglie wavelength λ_d, then ______

What is the de Broglie wavelength of a ball of mass 0.060 kg moving at a speed of 1.0 m/s?

A electron of mass me revolves around a nucleus of charge +Ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated wit it is expressed as `vecμ =−e/(2 m_e)vecL `, where `vec L` is the orbital angular momentum of the electron. Give the significance of negative sign.

State any one phenomenon in which moving particles exhibit wave nature.

Relativistic corrections become necessary when the expression for the kinetic energy `1/2 mv^2`, becomes comparable with mc², where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?

1. λ = 10 nm
2. λ = 10^–1 nm
3. λ = 10^–4 nm
4. λ = 10^–6 nm

A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.

Matter waves are ______.