Q96 / 110 · VITEEE 2022 · Physics

What is the ground state energy of positronium? (The ground state energy of hydrogen is \(-13.6 \mathrm{eV}\))

A
\(-3.4 \mathrm{eV}\)
Correct answer
B
\(-6.8 \mathrm{eV}\)
C
\(-13.6 \mathrm{eV}\)
D
\(-27.2 \mathrm{eV}\)

Solution

For positronium reduced mass \(=\frac{\mathrm{mm}}{\mathrm{m}+\mathrm{m}}\) \(=\frac{\mathrm{m}^2}{2 \mathrm{~m}}=\frac{\mathrm{m}}{2}\) Hence Rydberg's constant for positronium is half of that for hydrogen atom. Hence, ground state energy for positronium \(=-\frac{13.6}{2}=-6.8 \mathrm{eV}\)

Hence, the correct answer is option: 'B'.

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