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Photons of frequencies equal to the frequencies of `H_(beta) and H_(oo)` lines of hydrogen incident on a photosensitive plate, whose threshold frequency is equal to the frequency of `H_(alpha)` line of hydrogen. The ratio of the maximum kinetic energies of the emitted electrons is

A

`7:16`

B

`3:4`

C

`8:27`

D

`5:36`

Text Solution

Verified by Experts

The correct Answer is:
A
Energy of photons of `H_(alpha)" line "=Delta E(3 rarr 2)`
`=13.6 ((1)/(4)-(1)/(9))=(13.6xx5)/(36) =1.89 eV`
Energy of photons of `H_(beta)" line "=Delta E (4 rarr 2)`
`=13.6((1)/(4) -(1)/(16))=(12xx13.6)/(64) =2.55 eV`
Energy of photons of `H_(oo)" line "=Delta E(oo rarr 2)`
`=(13.6)/(4) =3.4 eV`
Ratio of kinetic energy of emitted photons
`=(255-1.89)/(3.4-1.89) =(0.66)/(1.51) ~~ (0.7)/(1.6) ~~ (7)/(16)`
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