The de-Broglie wavelength of an electron moving with a velocity c/2 (c = velocity of light in vacuum) is equal to the wavelength of a photon. The ratio of the kinetic energies of electron and photon is

• 1 : 4

• 1 : 2

• 1 : 1

• 2 : 1

Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

• $\frac{5}{27}$

• $\frac{3}{23}$

• $\frac{7}{29}$

• $\frac{9}{31}$

The ionization energy of hydrogen is 13.6 eV. The energy of the photon released when an electron jumps from the first excited state (n = 2) to the ground state of a hydrogen atom is

• 3.4 eV

• 4.53 eV

• 10.2 eV

• 13.6 eV

The de-Broglie wavelength of an electron is the same as that of a 50 keV X-ray photon. The ratio of the energy of the photon to the kinetic energy of the electron is (the energy equivalent of electron mass is 0.5 MeV)

• 1 : 50

• 1 : 20

• 20 : 1

• 50 : 1

Consider two particles of different masses. In which of the following situations the heavier of the two particles will have smaller de-Broglie wavelength ?

• Both have a free fall through the same height

• Both move with the same kinetic energy

• Both move with the same linear momentum

• Both move with the same speed