First slide

Bohr's atom model

Question

A particular hydrogen like atom has its ground state binding energy 122.4eV. If it is in ground state. Then:

Moderate

A

its atomic number is 3
B

an electron of 90 eV can excite it.
C

an electron of kinetic energy nearly 91.8 eV can be brought to almost rest by this atom.
D

an electron of kinetic energy 2.6 eV may emerge from the atom when electron of kinetic energy 125 eV collides with this atom.

Solution

$\begin{array}{l} 122 .4 = 13 .6 \times \frac{Z^{2}}{(1)^{2}} \Rightarrow Z = 3 \\ {ΔE}_{1 \to 2} = 13 .6 \times (3)^{2} [\frac{1}{1^{2}} - \frac{1}{2^{2}}] = 13 .6 \times 9 \times \frac{3}{4} \\ = 91 .8 eV . \\ 125 = 122 .4 + {K.E}_{\cdot e -} \\ \Rightarrow K \cdot E_{e^{-}} = 2 .6 eV \end{array}$

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