For Lyman series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength of Lyman series the energy difference in two levels showing transition should be maximum, (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)) \(\frac{{\rm{1}}}{{\rm{\lambda }}}{\rm{ = }}{{\rm{R}}_{\rm{H}}}\left[ {\frac{1}{{{1^2}}}{\rm{ - }}\frac{1}{{{\infty ^2}}}} \right]{\rm{ = 109678}}\) \(\therefore {\rm{\lambda = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}{\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)
CHXI02:STRUCTURE OF ATOM
307588
The wave number of the first emission line in the Balmer series of H-Spectrum is: (Rydberg constant):
1 \(\frac{{\rm{5}}}{{{\rm{36}}}}\,{\rm{R}}\)
2 \(\frac{{\rm{9}}}{{{\rm{400}}}}{\rm{R}}\)
3 \(\frac{{\rm{7}}}{{\rm{6}}}{\rm{R}}\)
4 \(\frac{{\rm{3}}}{{\rm{4}}}{\rm{R}}\)
Explanation:
For first line of Balmer series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 2}}\) and \({{\rm{n}}_2}{\rm{ = 3}}\). \({\rm{\bar v = R}}{{\rm{Z}}^{\rm{2}}}\left( {\frac{{\rm{1}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ - }}\frac{{\rm{1}}}{{{{\rm{3}}^{\rm{2}}}}}} \right){\rm{ = R}}\left( {\frac{{\rm{1}}}{{\rm{4}}}{\rm{ - }}\frac{{\rm{1}}}{{\rm{9}}}} \right){\rm{ = }}\frac{{{\rm{5R}}}}{{{\rm{36}}}}\)
JEE - 2013
CHXI02:STRUCTURE OF ATOM
307589
What transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion shall have the same wave number as the first line in Balmer series of H atom?
1 \({\rm{7}} \to {\rm{5}}\)
2 \({\rm{6}} \to {\rm{4}}\)
3 \({\rm{5}} \to {\rm{3}}\)
4 \({\rm{4}} \to {\rm{2}}\)
Explanation:
For H atom, first Balmer line in series is \({{\rm{E}}_{\rm{3}}}{\rm{ - }}{{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{3}} \right)}^{\rm{2}}}}}{\rm{ + }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\) For \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion \({\rm{(Z = 2)}}\) \({{\rm{E}}_{\rm{6}}}{\rm{ - }}{{\rm{E}}_{\rm{4}}}{\rm{ = - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{6}}^{\rm{2}}}}}{\rm{ - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{4}}^{\rm{2}}}}}\) \({\rm{ = - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\rm{2}}^{\rm{2}}}\left| {\frac{{{\rm{16 - 36}}}}{{{\rm{16 \times 36}}}}} \right|\) \({\rm{ = }}\frac{{{\rm{4 \times 20}}}}{{{\rm{36 \times 16}}}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\)
CHXI02:STRUCTURE OF ATOM
307590
The shortest wavelength in H spectrum of Lyman series when \({{\rm{R}}_{\rm{H}}}{\rm{ = 109678c}}{{\rm{m}}^{{\rm{ - 1}}}}\) is
For Lyman series \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength \({\rm{'\lambda '}}\) of Lyman series is the energy difference in two levels showing transition should be maximum (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)). \(\frac{1}{\lambda } = {R_H}\left[ {\frac{1}{{{1^2}}} - \frac{1}{{{\infty ^2}}}} \right]\) \( = 109678\) \(\therefore \lambda {\rm{ = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}\) \({\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)
For Lyman series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength of Lyman series the energy difference in two levels showing transition should be maximum, (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)) \(\frac{{\rm{1}}}{{\rm{\lambda }}}{\rm{ = }}{{\rm{R}}_{\rm{H}}}\left[ {\frac{1}{{{1^2}}}{\rm{ - }}\frac{1}{{{\infty ^2}}}} \right]{\rm{ = 109678}}\) \(\therefore {\rm{\lambda = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}{\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)
CHXI02:STRUCTURE OF ATOM
307588
The wave number of the first emission line in the Balmer series of H-Spectrum is: (Rydberg constant):
1 \(\frac{{\rm{5}}}{{{\rm{36}}}}\,{\rm{R}}\)
2 \(\frac{{\rm{9}}}{{{\rm{400}}}}{\rm{R}}\)
3 \(\frac{{\rm{7}}}{{\rm{6}}}{\rm{R}}\)
4 \(\frac{{\rm{3}}}{{\rm{4}}}{\rm{R}}\)
Explanation:
For first line of Balmer series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 2}}\) and \({{\rm{n}}_2}{\rm{ = 3}}\). \({\rm{\bar v = R}}{{\rm{Z}}^{\rm{2}}}\left( {\frac{{\rm{1}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ - }}\frac{{\rm{1}}}{{{{\rm{3}}^{\rm{2}}}}}} \right){\rm{ = R}}\left( {\frac{{\rm{1}}}{{\rm{4}}}{\rm{ - }}\frac{{\rm{1}}}{{\rm{9}}}} \right){\rm{ = }}\frac{{{\rm{5R}}}}{{{\rm{36}}}}\)
JEE - 2013
CHXI02:STRUCTURE OF ATOM
307589
What transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion shall have the same wave number as the first line in Balmer series of H atom?
1 \({\rm{7}} \to {\rm{5}}\)
2 \({\rm{6}} \to {\rm{4}}\)
3 \({\rm{5}} \to {\rm{3}}\)
4 \({\rm{4}} \to {\rm{2}}\)
Explanation:
For H atom, first Balmer line in series is \({{\rm{E}}_{\rm{3}}}{\rm{ - }}{{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{3}} \right)}^{\rm{2}}}}}{\rm{ + }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\) For \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion \({\rm{(Z = 2)}}\) \({{\rm{E}}_{\rm{6}}}{\rm{ - }}{{\rm{E}}_{\rm{4}}}{\rm{ = - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{6}}^{\rm{2}}}}}{\rm{ - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{4}}^{\rm{2}}}}}\) \({\rm{ = - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\rm{2}}^{\rm{2}}}\left| {\frac{{{\rm{16 - 36}}}}{{{\rm{16 \times 36}}}}} \right|\) \({\rm{ = }}\frac{{{\rm{4 \times 20}}}}{{{\rm{36 \times 16}}}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\)
CHXI02:STRUCTURE OF ATOM
307590
The shortest wavelength in H spectrum of Lyman series when \({{\rm{R}}_{\rm{H}}}{\rm{ = 109678c}}{{\rm{m}}^{{\rm{ - 1}}}}\) is
For Lyman series \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength \({\rm{'\lambda '}}\) of Lyman series is the energy difference in two levels showing transition should be maximum (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)). \(\frac{1}{\lambda } = {R_H}\left[ {\frac{1}{{{1^2}}} - \frac{1}{{{\infty ^2}}}} \right]\) \( = 109678\) \(\therefore \lambda {\rm{ = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}\) \({\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)
For Lyman series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength of Lyman series the energy difference in two levels showing transition should be maximum, (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)) \(\frac{{\rm{1}}}{{\rm{\lambda }}}{\rm{ = }}{{\rm{R}}_{\rm{H}}}\left[ {\frac{1}{{{1^2}}}{\rm{ - }}\frac{1}{{{\infty ^2}}}} \right]{\rm{ = 109678}}\) \(\therefore {\rm{\lambda = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}{\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)
CHXI02:STRUCTURE OF ATOM
307588
The wave number of the first emission line in the Balmer series of H-Spectrum is: (Rydberg constant):
1 \(\frac{{\rm{5}}}{{{\rm{36}}}}\,{\rm{R}}\)
2 \(\frac{{\rm{9}}}{{{\rm{400}}}}{\rm{R}}\)
3 \(\frac{{\rm{7}}}{{\rm{6}}}{\rm{R}}\)
4 \(\frac{{\rm{3}}}{{\rm{4}}}{\rm{R}}\)
Explanation:
For first line of Balmer series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 2}}\) and \({{\rm{n}}_2}{\rm{ = 3}}\). \({\rm{\bar v = R}}{{\rm{Z}}^{\rm{2}}}\left( {\frac{{\rm{1}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ - }}\frac{{\rm{1}}}{{{{\rm{3}}^{\rm{2}}}}}} \right){\rm{ = R}}\left( {\frac{{\rm{1}}}{{\rm{4}}}{\rm{ - }}\frac{{\rm{1}}}{{\rm{9}}}} \right){\rm{ = }}\frac{{{\rm{5R}}}}{{{\rm{36}}}}\)
JEE - 2013
CHXI02:STRUCTURE OF ATOM
307589
What transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion shall have the same wave number as the first line in Balmer series of H atom?
1 \({\rm{7}} \to {\rm{5}}\)
2 \({\rm{6}} \to {\rm{4}}\)
3 \({\rm{5}} \to {\rm{3}}\)
4 \({\rm{4}} \to {\rm{2}}\)
Explanation:
For H atom, first Balmer line in series is \({{\rm{E}}_{\rm{3}}}{\rm{ - }}{{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{3}} \right)}^{\rm{2}}}}}{\rm{ + }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\) For \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion \({\rm{(Z = 2)}}\) \({{\rm{E}}_{\rm{6}}}{\rm{ - }}{{\rm{E}}_{\rm{4}}}{\rm{ = - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{6}}^{\rm{2}}}}}{\rm{ - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{4}}^{\rm{2}}}}}\) \({\rm{ = - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\rm{2}}^{\rm{2}}}\left| {\frac{{{\rm{16 - 36}}}}{{{\rm{16 \times 36}}}}} \right|\) \({\rm{ = }}\frac{{{\rm{4 \times 20}}}}{{{\rm{36 \times 16}}}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\)
CHXI02:STRUCTURE OF ATOM
307590
The shortest wavelength in H spectrum of Lyman series when \({{\rm{R}}_{\rm{H}}}{\rm{ = 109678c}}{{\rm{m}}^{{\rm{ - 1}}}}\) is
For Lyman series \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength \({\rm{'\lambda '}}\) of Lyman series is the energy difference in two levels showing transition should be maximum (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)). \(\frac{1}{\lambda } = {R_H}\left[ {\frac{1}{{{1^2}}} - \frac{1}{{{\infty ^2}}}} \right]\) \( = 109678\) \(\therefore \lambda {\rm{ = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}\) \({\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)
For Lyman series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength of Lyman series the energy difference in two levels showing transition should be maximum, (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)) \(\frac{{\rm{1}}}{{\rm{\lambda }}}{\rm{ = }}{{\rm{R}}_{\rm{H}}}\left[ {\frac{1}{{{1^2}}}{\rm{ - }}\frac{1}{{{\infty ^2}}}} \right]{\rm{ = 109678}}\) \(\therefore {\rm{\lambda = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}{\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)
CHXI02:STRUCTURE OF ATOM
307588
The wave number of the first emission line in the Balmer series of H-Spectrum is: (Rydberg constant):
1 \(\frac{{\rm{5}}}{{{\rm{36}}}}\,{\rm{R}}\)
2 \(\frac{{\rm{9}}}{{{\rm{400}}}}{\rm{R}}\)
3 \(\frac{{\rm{7}}}{{\rm{6}}}{\rm{R}}\)
4 \(\frac{{\rm{3}}}{{\rm{4}}}{\rm{R}}\)
Explanation:
For first line of Balmer series, \({{\rm{n}}_{\rm{1}}}{\rm{ = 2}}\) and \({{\rm{n}}_2}{\rm{ = 3}}\). \({\rm{\bar v = R}}{{\rm{Z}}^{\rm{2}}}\left( {\frac{{\rm{1}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ - }}\frac{{\rm{1}}}{{{{\rm{3}}^{\rm{2}}}}}} \right){\rm{ = R}}\left( {\frac{{\rm{1}}}{{\rm{4}}}{\rm{ - }}\frac{{\rm{1}}}{{\rm{9}}}} \right){\rm{ = }}\frac{{{\rm{5R}}}}{{{\rm{36}}}}\)
JEE - 2013
CHXI02:STRUCTURE OF ATOM
307589
What transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion shall have the same wave number as the first line in Balmer series of H atom?
1 \({\rm{7}} \to {\rm{5}}\)
2 \({\rm{6}} \to {\rm{4}}\)
3 \({\rm{5}} \to {\rm{3}}\)
4 \({\rm{4}} \to {\rm{2}}\)
Explanation:
For H atom, first Balmer line in series is \({{\rm{E}}_{\rm{3}}}{\rm{ - }}{{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{3}} \right)}^{\rm{2}}}}}{\rm{ + }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\) For \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion \({\rm{(Z = 2)}}\) \({{\rm{E}}_{\rm{6}}}{\rm{ - }}{{\rm{E}}_{\rm{4}}}{\rm{ = - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{6}}^{\rm{2}}}}}{\rm{ - }}\frac{{{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\left( {\rm{2}} \right)}^{\rm{2}}}}}{{{{\rm{4}}^{\rm{2}}}}}\) \({\rm{ = - }}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ \times }}{{\rm{2}}^{\rm{2}}}\left| {\frac{{{\rm{16 - 36}}}}{{{\rm{16 \times 36}}}}} \right|\) \({\rm{ = }}\frac{{{\rm{4 \times 20}}}}{{{\rm{36 \times 16}}}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right){\rm{ = }}\frac{{{\rm{5}}{{\rm{E}}_{\rm{1}}}\left( {\rm{H}} \right)}}{{{\rm{36}}}}\)
CHXI02:STRUCTURE OF ATOM
307590
The shortest wavelength in H spectrum of Lyman series when \({{\rm{R}}_{\rm{H}}}{\rm{ = 109678c}}{{\rm{m}}^{{\rm{ - 1}}}}\) is
For Lyman series \({{\rm{n}}_{\rm{1}}}{\rm{ = 1}}\) For shortest wavelength \({\rm{'\lambda '}}\) of Lyman series is the energy difference in two levels showing transition should be maximum (i.e., \({{\rm{n}}_{\rm{2}}}{\rm{ = }}\infty \)). \(\frac{1}{\lambda } = {R_H}\left[ {\frac{1}{{{1^2}}} - \frac{1}{{{\infty ^2}}}} \right]\) \( = 109678\) \(\therefore \lambda {\rm{ = 911}}{\rm{.7 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}\) \({\rm{ = 911}}{\rm{.7}}\mathop {\rm{A}}\limits^{\rm{o}} \)