Question

A 12.5 eV electron beam is used to bombard gaseous hydrogen atroom temperature. What series of wavelengths will be emitted?

Answer 1

Given: An electron of 12.5 eV is used to bombard gaseous hydrogen atom at room temperature.

Energy of gaseous hydrogen atom in its ground state at room temperature is −13.6 eV.

The energy of gaseous hydrogen after bombardment of electron will be ( −13.6+12.5=−1.1 eV ).

If the energy is equal to the energy of the gaseous hydrogen, then electron has jumped from n=1 to n=3 level.

The orbital energy is given as,

E= −13.6 ( n ) 2  eV

By substituting the value of n in the above expression, we get,

E 1 = −13.6 ( 3 ) 2  eV =−1.5 eV

Relation for Lyman series is given as,

1 λ = R y ( 1 1 2 − 1 n 2 )(1)

where, Rydberg constant is R y and wavelength of the radiation is λ.

By substituting the value of n in the equation (1), we get,

1 λ =1.097× 10 7 ( 1 1 2 − 1 3 2 ) 1 λ =1.097× 10 7 × 8 9 λ= 9 8×1.097× 10 7 =102.55 nm

By substituting n=2 in the equation (1), we get,

1 λ =1.097× 10 7 ( 1 1 2 − 1 2 2 ) =1.097× 10 7 × 3 4 λ= 4 1.097× 10 7 ×3 =121.54 nm

The value of wavelength of radiation when electron jumps from n=3 to n=2 is given as,

1 λ =1.097× 10 7 ( 1 2 2 − 1 3 2 ) =1.097× 10 7 × 5 36 λ= 36 1.097× 10 7 ×5 =656.33 nm

Thus, the Lyman series of wavelength is 102.55 nm, 121.54 nm and 656.33 nm.