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Let vartheta(1) be the frequency of the ...

Let `vartheta_(1)` be the frequency of the series limit of the Lyman series and `vartheta_(2)` be the frequency of the first line of the Lyman series and `vartheta_(3)` be the frequency of the series limit of Balmar series, then

A

`vartheta_(1)-vartheta_(2)=vartheta_(3)`

B

`vartheta_(2)-vartheta_(1)=vartheta_(3)`

C

`2vartheta_(3)=vartheta_(1)+vartheta_(2)`

D

`vartheta_(1)+vartheta_(2)=vartheta_(3)`

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A
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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 orbits from higher energy orbits respectively (as shown in figure) Maximum number of lines produced when an electron jumps from nth level to ground level is equal to (n(n-1))/(2) . For example, in the case of n = 4, number of lines produced is 6. (4 rarr 3, 4 rarr 2, 4 rarr 1, 3 rarr 2, 3 rarr 1, 2 rarr 1) . When an electron returns from n_(2) to n_(1) state, the number of lines in the spectrum will be equal to ((n_(2) - n_(1))(n_(2)-n_(1) +1))/(2) If the electron comes back from energy level having energy E_(2) to energy level having energy E_(2) then the difference may be expressed in terms of energy of photon as E_(2) - E_(1) = Delta E, lambda = (h c)/(Delta E) . Since h and c are constant, Delta E corresponds to definite energy, thus each transition from one energy level to another will prouce a higher of definite wavelength. THis is actually observed as a line in the spectrum of hydrogen atom. Wave number of the line is given by the formula bar(v) = RZ^(2)((1)/(n_(1)^(2)) - (1)/(n_(2)^(2))) Where R is a Rydberg constant (R = 1.1 xx 10^(7)) (i) First line of a series : it is called .line of logest wavelength. or .line of shortest energy.. (ii) Series limit of last of a series : It is the line of shortest wavelength or line of highest energy. Let v_(1) be the frequency of the series limit of the Lyman series, v_(2) be the frequency of the first line of the Lyman series, and v_(3) be the frequency of the series limit of the Balmer series

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AAKASH SERIES-ATOMS-EXERCISE - II
  1. When the electron in hydrogen atom jumps from the second orbit to the...

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  2. The ratio of the largest to shortest wavelengths in Balmer series of h...

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  3. An electron in a hydrogen atom makes a transition n(l) rarr n(2), wher...

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  4. Any radiation in the ultra violet region of Hydrogen spectrum is able ...

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  5. A hydrogen atom emits a photon corresponding to an electron transtion ...

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  6. The wave number of energy emitted when electron jumbs from fourth orbi...

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  7. In a Bohr atom the electron is replaced by a particle of mass 150 time...

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  8. If the wavelength of first member of Balmer series of hydrogen spectru...

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  9. A hydrogen-like atom (atomic number Z) is in a higher excited state of...

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  10. Electrons from n = 2 to n= 1 in hydrogen atom is made to fall on a met...

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  11. Let vartheta(1) be the frequency of the series limit of the Lyman seri...

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  12. When a silver foil (Z = 47) was used in an alpha ray scattering exper...

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  13. In Rutherford experiments on alpha-ray scattering the number of partic...

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  14. An alpha nucleus of energy 1/2 m vartheta^(2) bombards a heavy nuclear...

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  15. In Rutherford's alpha particle scattering experiment with their gold f...

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  16. An alpha-particle of energy 5 Mev is scattered through 180^(@) by a fi...

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  17. The transition from the state n = 4 to n = 3 in a hydrogen like atom r...

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  18. Energy required for the electron excitation in Li++ from the first to ...

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  19. Hydrogen (""(1)H^(1)), Deuterium (""(1)H^(2)), singly ionized Helium (...

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