## Question

Moving with the same velocity, which of the following has the longest de Broglie wavelength?

### Solution

-particle is an electron. Since electron has the smallest mass, its de Broglie wavelength is the longest as the velocity of all particles is the same

#### SIMILAR QUESTIONS

The total energy (potential + kinetic) of an electron in the ground state of Bohr model of hydrogen atom is –13.6 eV. Obtain the values of the potential energy *U* and kinetic energy *K* in eV. Include –ve or +ve sign as required.

A muonic hydrogen atom is a bound state of a negatively-charged muon of mass 207*m _{e}* and a proton and the muon orbits around the proton. Obtain the radius of its first Bohr orbit.

The energy of an electron in an excited hydrogen atom is –3.4 eV. Calculate the angular momentum of the electron according to Bohr’s theory. Planck’s constant .

A hydrogen atom rises from its *n* = 1 state to the *n* = 4 state by absorbing energy. If the potential energy of the atom in *n* = 1 state be –13.6 eV, thencalculate : potential energy in *n* = 4 state.

The ionization energy of the hydrogen atom is given to be 13.6 eV. A photon falls on a hydrogen atom which is initially in the ground state and excites it to the *n* = 4 state. Calculate the wavelength of the photon.

An electron of energy 20 eV collides with a hydrogen atom in the ground state. As a result, the atom is excited to a higher energy state and the electron is scattered with reduced velocity. The atom subsequently returns to its ground state with emission of radiation of wavelength . Find the velocity of the scattered electron.

A proton captures a free electron whose kinetic energy is zero and forms a hydrogen atom of lowest energy-level (*n* = 1). If a photon is emitted in this process, what will be the wavelength of radiation? In which region of electromagnetic spectrum, will this radiation fall? (Ionisation potential of hydrogen atom = 13.6 V, ).

The de Broglie wavelength of a neutron at 927^{o}C is . What will be its wavelength at 27^{o}C?

What is the de Broglie wavelength of an electron of energy 1800 eV? Mass of electron and Planck’s constant .

The de Broglie wavelength of an electron moving with a velocity is equal to that a photon. The ratio of the kinetic energy of the electron to that of the photon is