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Wave Optics

Question
CBSEENPH12038568
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A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

Solution
In ground state, energy of gaseous hydrogen at room temperature = – 13.6 eV.

Energy of electron beam used to bombard the gaseous hydrogen = 12.5 eV 

Therefore, after bombardment,
Energy of gaseous hydrogen = –13.6 + 12.6
                                           = – 1.1 eV.

Since, En = -13.6n2       
 So,          n2 = -13.6-1.1 = 12.3    ⇒    n  = 3 

That is, the electron would jump from n = 1 to n = 3, where E3 = -13.632 = -1.5 eV. 
On de-excitation, the electron may jump from n = 3 to n = 2 giving rise to Balmer series.

It may also jump from n = 3 to n = 1, giving rise to Lyman series. 


So, number of spectral line is,

= n(n-1)2 = 3(3-1)2 = 3 

Thus, three spectral lines appear.

Some More Questions From Wave Optics Chapter

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson's model much less, about the same, or much greater than that predicted by Rutherford's model?

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of α-particles by a thin foil?

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