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.

What will be the de Broglie wavelength (in metres) of an electron moving with a velocity of 1.2 × 10⁵ m s^–1?

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

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.

When light of wavelength 248 nm falls on a metal of threshold energy 3.0 eV, the de-Broglie wavelength of emitted electrons is ______ A°. (Round off to the Nearest Integer)

[Use: `sqrt3` = 1.73, h = 6.63 × 10⁻³⁴ Js, m_e = 9.1 × 10⁻³¹ kg, c = 3.0 × 10⁸ ms⁻¹, 1eV = 1.6 × 10⁻¹⁹ J]

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.

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

A proton and a Li³⁺ nucleus are accelerated by the same potential. If λ_Li and λ_P denote the de Broglie wavelengths of Li³⁺ and proton respectively, then the value of `λ_("Li")/(λ_"P")` is x × 10⁻¹. The value of x is ______. [Rounded-off to the nearest integer]

[Mass of Li³⁺ = 8.3 mass of proton]