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 $=13.6\times {\text{z}}^2\text{eV}$
$\Rightarrow \text{z}=\sqrt{\frac{\text{122.4}}{\text{13.6}}}=3$
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.