Test Index

Atoms and Nuclei

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In a mixture of H and

He^{+}

gases (

He^{+}

is singly ionized He atom), H atoms and

He^{+}

ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to

He^{+}

ions (by collision). Assume that the Bohr model of atom is exactly valid.

Section: Physics

Question : 50 of 53

Marks: +1, -0

\mathrm{He}^{+}

Solution:

Initially, for H atoms, we have

E_{2}

\left(\frac{-13.6}{2^{2}}\right)1^{2}

\left(\frac{-13.6}{4}\right)

Therefore,

E_{1}

= 13.6 eV. Also, for

\mathrm{He}^{+}

atoms, we have

E_{2}

\frac{-13.6}{2^{2}} \times 2^{2}

= - 13.6 eV

The excitation energy for H atoms is

E_{2}-E_{1}

\left(\frac{-13.6}{4}\right) + 13.6

= 10.2 eV

After collision, the energy of

\mathrm{He}^{+}

atoms is

- 13.6 + 10.2 = - 3.4 =

\frac{-13.6 \times 2^{4}}{n^{2}}

⇒

n^{2}

\frac{13.6 \times 4}{13.4}

= 16 ⇒ n = 4

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