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Question
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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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
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