NEET-XII-Physics
11: Dual Nature Of Radiation And Matter
- #14The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which
(a) an electron, and
(b) a neutron, would have the same de Broglie wavelength.Ans : Wavelength of light of a sodium line, λ = 589 nm = 589 × 10-9 m
Mass of an electron, me= 9.1 × 10-31 kg
Mass of a neutron, mn= 1.66 × 10-27 kg
Planck’s constant, h = 6.6 × 10-34 Js
(a) For the kinetic energy K, of an electron accelerating with a velocity v, we have the relation:
We have the relation for de Broglie wavelength as:
Substituting equation (2) in equation (1), we get the relation:
Hence, the kinetic energy of the electron is 6.9 × 10-25 J or 4.31 μeV.
(b) Using equation (3), we can write the relation for the kinetic energy of the neutron as:
Hence, the kinetic energy of the neutron is 3.78 × 10-28 J or 2.36 neV.
- #14-aan electron, andAns : For the kinetic energy K, of an electron accelerating with a velocity v, we have the relation:
We have the relation for de Broglie wavelength as:
Substituting equation (2) in equation (1), we get the relation:
Hence, the kinetic energy of the electron is 6.9 × 10-25 J or 4.31 μeV.
- #14-ba neutron, would have the same de Broglie wavelength.Ans : Using equation (3), we can write the relation for the kinetic energy of the neutron as:
Hence, the kinetic energy of the neutron is 3.78 × 10-28 J or 2.36 neV.