A proton and an α-particle are accelerated, using the same potential difference. How are the de Broglie wavelengths λ_p and λ_a related to each other?

Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency v is used to convert 1kg of ice at 0°C to water at 0°C. Then, the time T taken for the conversion

A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values λ₁, λ₂ with λ₁ > λ₂. Which of the following statement are true?

(i) In the explanation of photo electric effect, we assume one photon of frequency v collides with an electron and transfers its energy. This leads to the equation for the maximum energy E_max of the emitted electron as

where ϕ₀ is the work function of the metal. If an electron absorbs 2 photons (each of frequency v) what will be the maximum energy for the emitted electron?

(ii) Why is this fact (two photon absorption) not taken into consideration in our discussion of the stopping potential?

There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength.