Q63 / 69 · JEE Advanced 2008 (Paper 1) · Physics

Paragraph: In a mixture of $\mathrm{H}-\mathrm{H}^{+}$gas $\left(\mathrm{He}^{+}\right.$is singly ionised $\mathrm{He}$ atom), $\mathrm{H}$ atoms and $\mathrm{He}^{+}$ions are excited to their respective first excited states. Subsequently, $\mathrm{H}$ atoms transfer their total excitation energy to $\mathrm{He}^{+}$ions (by collisions). Assume that the Bohr model of atom is exactly valid.Question: The ratio of the kinetic energy of the $n=2$ electron for the $\mathrm{H}$ atom to that of $\mathrm{He}^{+}$ ion is

  • Correct answer
    A
    $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • C
    1
  • D
    2

Solution

Kinetic energy $K \propto Z^2$ $$ \frac{K_H}{K_{\mathrm{He}^{+}}}=\left(\frac{1}{2}\right)^2=\frac{1}{4} $$ $\therefore$ correct option is (a).

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

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