Advertisement Remove all ads

Electrons Are Emitted from an Electron Gun at Almost Zero Velocity and Are Accelerated by an Electric Field E Through a Distance of 1.0 M. the Electrons Are Now Scattered by an - Physics

Sum

Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen?

Advertisement Remove all ads

Solution

Given:

Distance travelled by the electron, d = 1.0 m

Wavelength of red light ,λ = 656.3 nm = 656.3 × 10^-9 m

Since the given wavelength lies in Balmer series, the transition that requires minimum energy is from n1 = 3 to n2 = 2.
Energy of this transition will be equal to the energy (E) that will be required for the transition from the ground state to n = 3.

`E_1 = 13.6 (1/n_1^2 1/n_2^2)`

`rArr E_1 = 13.6 (1 - 1/9)`

`= (13.6xx8)/9 = 12.09 eV`

Energy, E (eV) = 12.09 eV 

∴ `V = 12.09 V`

Electric field, `E = V/d = 12.09/1 = 12.09 V//m`

 ∴ Minimum value of the electric field = 12.09 V/m = 12.1 V/m

Concept: The Line Spectra of the Hydrogen Atom
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 21 Bohr’s Model and Physics of Atom
Q 32 | Page 385
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×