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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


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?

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