307574
Electronic transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion takes from \({{\rm{n}}_{\rm{2}}}\) to \({{\rm{n}}_1}\) shell when electron transition to \({{\rm{1}}^{{\rm{st}}}}\) shell from 5th shell, the number of spectral line formed are
1 \({\rm{21}}\)
2 \({\rm{15}}\)
3 \({\rm{20}}\)
4 \({\rm{10}}\)
Explanation:
Number of lines \({\rm{ = }}\frac{{{\rm{n}}\left( {{\rm{n + 1}}} \right)}}{{\rm{2}}}\) where, \({\rm{n = }}{{\rm{n}}_{\rm{2}}}{\rm{ - }}{{\rm{n}}_{\rm{1}}}{\rm{ = 5 - 1 = 4}}{\rm{.}}\) No. of lines \(\frac{{{\rm{4 \times 5}}}}{{\rm{2}}}{\rm{ = 10}}{\rm{.}}\)
CHXI02:STRUCTURE OF ATOM
307575
Which transition in the hydrogen atomic spectrum will have the same wavelength as the Balmer transition (i.e. \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\) ) of \(\mathrm{\mathrm{He}^{+}}\) spectrum?
1 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=3}\)
2 \(\mathrm{\mathrm{n}=3}\) to \(\mathrm{\mathrm{n}=2}\)
3 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\)
4 \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\)
Explanation:
\(\mathrm{\because \dfrac{1}{\lambda}=Z^{2} \cdot R\left[\dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}}\right]}\) \(\mathrm{\therefore}\) For \(\mathrm{\mathrm{He}^{+}}\)ion, \(\mathrm{\mathrm{Z}=2, \mathrm{n}_{1}=2, \mathrm{n}_{2}=4}\) \(\frac{1}{\lambda }{\text{ = }}{{\text{2}}^{\text{2}}}{\text{.R}}\left[ {\frac{{\text{1}}}{{{{\text{2}}^{\text{2}}}}}{\text{ - }}\frac{{\text{1}}}{{{{\text{4}}^{\text{2}}}}}} \right]\) \(\frac{{\text{1}}}{\lambda }{\text{ = 4}} \times {\text{R}} \times \frac{{\text{3}}}{{{\text{16}}}}{\text{ = }}\frac{{\text{3}}}{{\text{4}}}{\text{R}}\) The same value of for \(\mathrm{\mathrm{H}}\)-atom is possible when electron jumps from \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\), i.e. \(\mathrm{\dfrac{1}{\lambda}=1^{2} \times \mathrm{R}\left[\dfrac{1}{1^{2}}-\dfrac{1}{2^{2}}\right]}\) \(\mathrm{\Rightarrow=1 \mathrm{R}\left[\dfrac{1}{1}-\dfrac{1}{4}\right]=\dfrac{3}{4} \mathrm{R}}\)
AIIMS - 2017
CHXI02:STRUCTURE OF ATOM
307576
The ionization enthalpy of hydrogen atom is \({\rm{1}}{\rm{.312 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{J/mol}}\). The energy required to excite the elctron in the atom from to \({\rm{n = 1}}\,\,{\rm{to}}\,\,{\rm{n = 2}}\) is
307577
Monochromatic radiation of specific wavelength is incident on H-atoms in ground state. H-atoms absorb energy and emit subsequently radiations of six different wavelength. Find wavelength of incident radiations:
307574
Electronic transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion takes from \({{\rm{n}}_{\rm{2}}}\) to \({{\rm{n}}_1}\) shell when electron transition to \({{\rm{1}}^{{\rm{st}}}}\) shell from 5th shell, the number of spectral line formed are
1 \({\rm{21}}\)
2 \({\rm{15}}\)
3 \({\rm{20}}\)
4 \({\rm{10}}\)
Explanation:
Number of lines \({\rm{ = }}\frac{{{\rm{n}}\left( {{\rm{n + 1}}} \right)}}{{\rm{2}}}\) where, \({\rm{n = }}{{\rm{n}}_{\rm{2}}}{\rm{ - }}{{\rm{n}}_{\rm{1}}}{\rm{ = 5 - 1 = 4}}{\rm{.}}\) No. of lines \(\frac{{{\rm{4 \times 5}}}}{{\rm{2}}}{\rm{ = 10}}{\rm{.}}\)
CHXI02:STRUCTURE OF ATOM
307575
Which transition in the hydrogen atomic spectrum will have the same wavelength as the Balmer transition (i.e. \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\) ) of \(\mathrm{\mathrm{He}^{+}}\) spectrum?
1 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=3}\)
2 \(\mathrm{\mathrm{n}=3}\) to \(\mathrm{\mathrm{n}=2}\)
3 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\)
4 \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\)
Explanation:
\(\mathrm{\because \dfrac{1}{\lambda}=Z^{2} \cdot R\left[\dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}}\right]}\) \(\mathrm{\therefore}\) For \(\mathrm{\mathrm{He}^{+}}\)ion, \(\mathrm{\mathrm{Z}=2, \mathrm{n}_{1}=2, \mathrm{n}_{2}=4}\) \(\frac{1}{\lambda }{\text{ = }}{{\text{2}}^{\text{2}}}{\text{.R}}\left[ {\frac{{\text{1}}}{{{{\text{2}}^{\text{2}}}}}{\text{ - }}\frac{{\text{1}}}{{{{\text{4}}^{\text{2}}}}}} \right]\) \(\frac{{\text{1}}}{\lambda }{\text{ = 4}} \times {\text{R}} \times \frac{{\text{3}}}{{{\text{16}}}}{\text{ = }}\frac{{\text{3}}}{{\text{4}}}{\text{R}}\) The same value of for \(\mathrm{\mathrm{H}}\)-atom is possible when electron jumps from \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\), i.e. \(\mathrm{\dfrac{1}{\lambda}=1^{2} \times \mathrm{R}\left[\dfrac{1}{1^{2}}-\dfrac{1}{2^{2}}\right]}\) \(\mathrm{\Rightarrow=1 \mathrm{R}\left[\dfrac{1}{1}-\dfrac{1}{4}\right]=\dfrac{3}{4} \mathrm{R}}\)
AIIMS - 2017
CHXI02:STRUCTURE OF ATOM
307576
The ionization enthalpy of hydrogen atom is \({\rm{1}}{\rm{.312 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{J/mol}}\). The energy required to excite the elctron in the atom from to \({\rm{n = 1}}\,\,{\rm{to}}\,\,{\rm{n = 2}}\) is
307577
Monochromatic radiation of specific wavelength is incident on H-atoms in ground state. H-atoms absorb energy and emit subsequently radiations of six different wavelength. Find wavelength of incident radiations:
307574
Electronic transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion takes from \({{\rm{n}}_{\rm{2}}}\) to \({{\rm{n}}_1}\) shell when electron transition to \({{\rm{1}}^{{\rm{st}}}}\) shell from 5th shell, the number of spectral line formed are
1 \({\rm{21}}\)
2 \({\rm{15}}\)
3 \({\rm{20}}\)
4 \({\rm{10}}\)
Explanation:
Number of lines \({\rm{ = }}\frac{{{\rm{n}}\left( {{\rm{n + 1}}} \right)}}{{\rm{2}}}\) where, \({\rm{n = }}{{\rm{n}}_{\rm{2}}}{\rm{ - }}{{\rm{n}}_{\rm{1}}}{\rm{ = 5 - 1 = 4}}{\rm{.}}\) No. of lines \(\frac{{{\rm{4 \times 5}}}}{{\rm{2}}}{\rm{ = 10}}{\rm{.}}\)
CHXI02:STRUCTURE OF ATOM
307575
Which transition in the hydrogen atomic spectrum will have the same wavelength as the Balmer transition (i.e. \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\) ) of \(\mathrm{\mathrm{He}^{+}}\) spectrum?
1 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=3}\)
2 \(\mathrm{\mathrm{n}=3}\) to \(\mathrm{\mathrm{n}=2}\)
3 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\)
4 \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\)
Explanation:
\(\mathrm{\because \dfrac{1}{\lambda}=Z^{2} \cdot R\left[\dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}}\right]}\) \(\mathrm{\therefore}\) For \(\mathrm{\mathrm{He}^{+}}\)ion, \(\mathrm{\mathrm{Z}=2, \mathrm{n}_{1}=2, \mathrm{n}_{2}=4}\) \(\frac{1}{\lambda }{\text{ = }}{{\text{2}}^{\text{2}}}{\text{.R}}\left[ {\frac{{\text{1}}}{{{{\text{2}}^{\text{2}}}}}{\text{ - }}\frac{{\text{1}}}{{{{\text{4}}^{\text{2}}}}}} \right]\) \(\frac{{\text{1}}}{\lambda }{\text{ = 4}} \times {\text{R}} \times \frac{{\text{3}}}{{{\text{16}}}}{\text{ = }}\frac{{\text{3}}}{{\text{4}}}{\text{R}}\) The same value of for \(\mathrm{\mathrm{H}}\)-atom is possible when electron jumps from \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\), i.e. \(\mathrm{\dfrac{1}{\lambda}=1^{2} \times \mathrm{R}\left[\dfrac{1}{1^{2}}-\dfrac{1}{2^{2}}\right]}\) \(\mathrm{\Rightarrow=1 \mathrm{R}\left[\dfrac{1}{1}-\dfrac{1}{4}\right]=\dfrac{3}{4} \mathrm{R}}\)
AIIMS - 2017
CHXI02:STRUCTURE OF ATOM
307576
The ionization enthalpy of hydrogen atom is \({\rm{1}}{\rm{.312 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{J/mol}}\). The energy required to excite the elctron in the atom from to \({\rm{n = 1}}\,\,{\rm{to}}\,\,{\rm{n = 2}}\) is
307577
Monochromatic radiation of specific wavelength is incident on H-atoms in ground state. H-atoms absorb energy and emit subsequently radiations of six different wavelength. Find wavelength of incident radiations:
307574
Electronic transition in \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion takes from \({{\rm{n}}_{\rm{2}}}\) to \({{\rm{n}}_1}\) shell when electron transition to \({{\rm{1}}^{{\rm{st}}}}\) shell from 5th shell, the number of spectral line formed are
1 \({\rm{21}}\)
2 \({\rm{15}}\)
3 \({\rm{20}}\)
4 \({\rm{10}}\)
Explanation:
Number of lines \({\rm{ = }}\frac{{{\rm{n}}\left( {{\rm{n + 1}}} \right)}}{{\rm{2}}}\) where, \({\rm{n = }}{{\rm{n}}_{\rm{2}}}{\rm{ - }}{{\rm{n}}_{\rm{1}}}{\rm{ = 5 - 1 = 4}}{\rm{.}}\) No. of lines \(\frac{{{\rm{4 \times 5}}}}{{\rm{2}}}{\rm{ = 10}}{\rm{.}}\)
CHXI02:STRUCTURE OF ATOM
307575
Which transition in the hydrogen atomic spectrum will have the same wavelength as the Balmer transition (i.e. \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\) ) of \(\mathrm{\mathrm{He}^{+}}\) spectrum?
1 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=3}\)
2 \(\mathrm{\mathrm{n}=3}\) to \(\mathrm{\mathrm{n}=2}\)
3 \(\mathrm{\mathrm{n}=4}\) to \(\mathrm{\mathrm{n}=2}\)
4 \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\)
Explanation:
\(\mathrm{\because \dfrac{1}{\lambda}=Z^{2} \cdot R\left[\dfrac{1}{n_{1}^{2}}-\dfrac{1}{n_{2}^{2}}\right]}\) \(\mathrm{\therefore}\) For \(\mathrm{\mathrm{He}^{+}}\)ion, \(\mathrm{\mathrm{Z}=2, \mathrm{n}_{1}=2, \mathrm{n}_{2}=4}\) \(\frac{1}{\lambda }{\text{ = }}{{\text{2}}^{\text{2}}}{\text{.R}}\left[ {\frac{{\text{1}}}{{{{\text{2}}^{\text{2}}}}}{\text{ - }}\frac{{\text{1}}}{{{{\text{4}}^{\text{2}}}}}} \right]\) \(\frac{{\text{1}}}{\lambda }{\text{ = 4}} \times {\text{R}} \times \frac{{\text{3}}}{{{\text{16}}}}{\text{ = }}\frac{{\text{3}}}{{\text{4}}}{\text{R}}\) The same value of for \(\mathrm{\mathrm{H}}\)-atom is possible when electron jumps from \(\mathrm{\mathrm{n}=2}\) to \(\mathrm{\mathrm{n}=1}\), i.e. \(\mathrm{\dfrac{1}{\lambda}=1^{2} \times \mathrm{R}\left[\dfrac{1}{1^{2}}-\dfrac{1}{2^{2}}\right]}\) \(\mathrm{\Rightarrow=1 \mathrm{R}\left[\dfrac{1}{1}-\dfrac{1}{4}\right]=\dfrac{3}{4} \mathrm{R}}\)
AIIMS - 2017
CHXI02:STRUCTURE OF ATOM
307576
The ionization enthalpy of hydrogen atom is \({\rm{1}}{\rm{.312 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{J/mol}}\). The energy required to excite the elctron in the atom from to \({\rm{n = 1}}\,\,{\rm{to}}\,\,{\rm{n = 2}}\) is
307577
Monochromatic radiation of specific wavelength is incident on H-atoms in ground state. H-atoms absorb energy and emit subsequently radiations of six different wavelength. Find wavelength of incident radiations:
