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Bohr's Model of Atom

The ionizatio...

Question

The ionization energy of a hydrogen-like ion $A$ is greater than that of another hydrogen-like ion $B$ . Let $u$ and $E$ represent the speed of the electron and energy of the atom respectively in the ground state. Then,

A

r_{A} > r_{B}

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B

u_{A} > u_{B}

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C

E_{A} > E_{B}

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D

L_{A} > L_{B}

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Solution

The correct option is A $u_{A} > u_{B}$
We know
$E = - 13.6 \frac{Z^{2}}{n^{2}} e V$
So Ionization energy $= 13.6 \frac{Z^{2}}{n^{2}} e V$
given, $I E_{A} > I E_{B},$ so $E_{A} < E_{B}$
that means $Z_{A} > Z_{B}$
Now $u \propto \frac{Z}{n}$
$u_{A} > u_{B}$

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