First slide

Hydrogen -like ion

Question

An alpha particle and a free electron both initially at rest combine to form a He - ion in its ground state with the emission of a single photon. The energy of the photon is

Moderate

A

54.4 eV
B

27.2 eV
C

13.6 eV
D

40.8 eV

Solution

For He - ion, the charge on the nucleus Z = 2
Energy is proportional to Z²
For hydrogen atom with Z = 1, the ground state energy is 13.6 eV.
For He- ion, ground state energy $= {Z^2} \times 13.6 = 4 \times 13.6 = 54.4eV\$

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