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CBSE Class 12 Physics 2016 Outside Delhi Set 1 Paper

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Question : 9 of 26
Marks: +1, -0
Define ionization energy.
How would the ionization energy change when electron in hydrogen atom is replaced by a particle of mass 200 times that of the electron but having the same charge?
OR
Calculate the shortest wavelength of the spectral lines emitted in Balmer series.
[Given Rydberg constant, R=107m−1R = 10^7 \mathrm{m}^{-1} ]
Solution:  
Definition
Formula
Calculation and Result
The minimum energy, required to free the electron from the ground state of the hydrogen atom, is known as Ionization Energy.
E0=me48ε02h2 i.e., E0∝mE_0 = \frac{m e^4}{8 \varepsilon_0^2 h^2} \text{ i.e., } E_0 \propto m
Therefore, Ionization Energy will become 200 times.
OR
Formula
Calculation and Result
1λ=R(122−1α2)\frac{1}{\lambda} = R \left( \frac{1}{2^2} - \frac{1}{\alpha^2} \right)
For shortest wavelength, n=an = a
Therefore, 1λ=R4=⇒l=4R=4×10−7m\frac{1}{\lambda} = \frac{R}{4} = \Rightarrow l = \frac{4}{R} = 4 \times 10^{-7} \mathrm{m}
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