A single electron orbit around a stationary nucleus of charge `+ Ze` where Z is a constant and e is the magnitude of the electronic charge. It requires`47.2 eV` to excite the electron from the second bohr orbit to the third bohr orbit. Find
(i) The value of Z
(ii) The energy required by nucleus to excite the electron from the third to the fourth bohr orbit
(iii) The wavelength of the electronmagnetic radiation required to remove the electron from the first bohr orbit to inlinity
(iv) The energy potential energy potential energy and the angular momentum of the electron in the first bohr orbit
(v) The radius of the first bohr orbit (The ionization energy of hydrogen atom ` = 13.6 eV ` bohr radius `= 5.3 xx 10^(-11) matre` velocity of light `= 3 xx 10^(8) m//sec` planks 's constant ` = 6.6 xx 10^(-34)` jules - sec )

Explanation

To solve the problem step by step, we will break down each part of the question.

### Given Data:
- Energy required to excite from the second to the third orbit: \( \Delta E = 47.2 \, \text{eV} \)
- Ionization energy of hydrogen: \( E_1 = 13.6 \, \text{eV} \)
- Bohr radius: \( r_0 = 5.3 \times 10^{-11} \, \text{m} \)
- Planck's constant: \( h = 6.63 \times 10^{-34} \, \text{J s} \)
- Speed of light: \( c = 3 \times 10^8 \, \text{m/s} \)
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