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The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electron returns to the third, fourth and fifth orbits from higher energy orbits respectively. The maximum number of lines produced when an electron jumps from nth level to ground level is equal Maximum number of lines produced when an electron jumps from nth level to ground level is equal to. 1(n1)2. For example, in the case of n=4, number of lines produces is 6. (43,42,41,32,31,21). When an electron returns from to state, the number of lines in the spectrum will be equal to (n2n1)(n2n1+1)2 If the electron comes back from energy level having energy to energy level having energy, then the difference may be expressed in the terms of energy of photon as E2E1ΔE,λ=hcΔE Since h and c are constants, ΔE corresponds to definite energy; thus each transition from one energy level to another will produce a light of definite wavelength. This is observed as a line in the spectrum of the hydrogen atom. Wavenumber of line is given by the formula ¯v=(1n211n22). where R is a Rydberg's constant (R=1.1×107m1)

The energy photon emitted corresponding to transition n = 3 to n=1 is:
[h=6×1034Jsec]

A
1.76×1018 J
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B
1.98×1018 J
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C
1.76×1017 J
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D
None of these
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Solution

The correct option is A 1.76×1018 J
Energy transition is,
¯v×hc=hc×R×Z2(1n211n22)

=6×1034×3×108×1.1×107×(119)

=1.76×1018 J

Option A is correct.

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Q. When energy is supplied to an atom, the electrons of the atom move to higher energy orbits depending on the amount of energy absorbed. When these electrons return to any of the lower energy orbits, they emit energy. Depending on whether the electrons return to the 1st, 2nd, 3rd, 4th or 5th orbits, the series formed are called Lyman, Balmer, Paschen, Brackett and Pfund series respectively.
If the electron comes back from the energy level E2 to the energy level E1, then the difference may be expressed in terms of the energy of photon as
E2E1=ΔE, λ=hcΔE
Thus each transition from one energy level to another will produce a light of definite wavelength. This is observed as a line in the spectrum of the hydrogen atom.
Wave number of the line is given by the formula
ν=RZ2(1n211n22)
Where R=1.097×105 cm1 is Rydberg constant.
List - IList - II(I) If the ionisation potential for hydrogen-like atom(P) 5.48×1032cR Jin a sample is 122.0 eV, then the energy of the lastline of Paschen series for this atom is:(II) In a single isolated atom, an electron makes (Q) 6.6×1032cR Jtransition from fifth excited state such that no spectral lines are observed in the visible range then maximum number of different types of photons observed is:(III) The difference in energy of the second line(R) 6of Lyman series and last line of Brackett series in ahydrogen sample is:(IV) The energy of the electromagnetic radiation(S) 4emitted during the transition of electron in betweenthe two levels of Li2+ ion whose principal quantumnumber sum is 4 and difference is 2 is:(T) 6.6×1034cR J(U) 0.53×1030cR J

Which of the following options has the correct combination considering List-I and List-II?
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