Question

A particular hydrogen like atom has its ground state binding energy $= 122.4 \, \, \text{eV} \text{.}$ It is in ground state. Then,

• A. its atomic number is $5$
• B. an electron of $90 \, \, \text{eV}$ can excite it
• C. an electron of kinetic energy $45.9 \, \, \text{eV}$ can be brought to almost rest by this atom
• D. an electron of kinetic energy nearly $2.6 \, \, \text{eV}$ may emerge from the atom when electron of kinetic energy $125 \, \, \text{eV}$ collides with this atom

Answer 1

Answer: (D)

Ground state binding energy $= 13.6 \times \text{z}^{2} \, \, \text{eV}$
$⇒ \, \, \, \text{z} = \sqrt{\frac{\text{122.4}}{\text{13.6}}} = 3$
The first excitation energy
$\Delta \mathrm{E}=13.6 \times \mathrm{z}^2 \times\left(1-\frac{1}{4}\right) \mathrm{eV}=91.8 \mathrm{eV}$
$\text{K} \text{.E}_{max} = 125 - 122.4 = 2.6 \, \, \text{eV}$
Hence, $90 \, \, \text{eV}$ electron cannot excite it.