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PhysicsModern PhysicsAtomic structureMedium2 minPYQ_2021

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Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?

Answer:

Solution:

Energy of $H$ -atom is $E = - 13.6 Z^{2} / n^{2}$ for $H$ -atom $Z = 1$ and for ground state, $n = 1$

$\Rightarrow E = - 13.6 \times \frac{1^{2}}{1^{2}} = - 13.6 e V$

Now for carbon atom (single ionised), $Z = 6$

$E = - 13.6 \frac{Z^{2}}{n^{2}} = - 13.6$ (given)

$\Rightarrow n^{2} = 6^{2} \Rightarrow n = 6$

Stream:JEESubject:PhysicsTopic:Modern PhysicsSubtopic:Atomic structure

⏱ 2mℹ️ Source: PYQ_2021

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