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2. structure of atom — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistry2. structure of atom1 Mark
MCQ
Positronium consists of an electron and a positron (a particle which has the same mass as an electron, but opposite charge) orbiting round their common centre of mass. Calculate the value of the Rydberg constant for this system.
  • A
    ${R_\infty }/4$
  • ✓
    ${R_\infty }/2$
  • C
    $2{R_\infty }$
  • D
    ${R_\infty }$
✓

Answer

Correct option: B.
${R_\infty }/2$
b
All to Bethe $-$ Salpeter equation:

$E_n=-\frac{\mu q_e^4}{8 h^2 E_0^2} \frac{1}{n^2}$

$\mu=$ reduced mass for positronium

$\mu=\frac{m_e+m_p}{m_e m_p}=\frac{m_e}{2}$

Final equation is

$E=-\frac{1}{2} \frac{m_e q_e^4}{8 h^2 E_0^2} \frac{1}{n^2}$

$R =\frac{ m _{ e } q _{ e }^4}{8 h ^2 E _0^2}$

For the above system $R_H=\frac{R}{2}$

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