A hydrogen atom in the ground state is given | vedclass

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(D) The energy of the ground state of a hydrogen atom is $E_1 = -13.6 \ eV$.When an energy of $10.2 \ eV$ is provided,the new energy level $E_n$ is gi

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(D) The energy of the ground state of a hydrogen atom is $E_1 = -13.6 \ eV$.When an energy of $10.2 \ eV$ is provided,the new energy level $E_n$ is given by $E_n = E_1 + 10.2 \ eV = -13.6 \ eV + 10.2 \ eV = -3.4 \ eV$.Since $E_n = -13.6/n^2 \ eV$,we have $-3.4 = -13.6/n^2$,which gives $n^2 = 4$,so $n = 2$.The electron is excited to the first excited state $(n = 2)$.The number of spectral lines emitted when an electron transitions from state $n$ to the ground state is given by the formula $N = n(n-1)/2$.For $n = 2$,$N = 2(2-1)/2 = 1$.Therefore,only $1$ spectral line will be emitted.

$A$ hydrogen atom in the ground state is given an energy of $10.2 \ eV$. How many spectral lines will be emitted due to the transition of electrons?

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