Question

In a hydrogen like sample electron is in $2nd$ excited state, the binding energy of $4th$ state of this sample is $-13.6eV$, then incorrect statement is :

• A. Atomic number of element is $4$.
• B. $3$ different types of spectral line will be observed if electrons make transition upto ground state from the $2nd$ excited state.
• C. A $25eV$ photon can set free the electron from the $2nd$ excited state of this sample.
• D. $2nd$ line of Balmer series of this sample has same energy value as $1st$ excitation energy of $H-$atoms.

Answer 1

The correct option is D $2nd$ line of Balmer series of this sample has same energy value as $1st$ excitation energy of $H-$atoms.

As we know,

$E=-13.6\frac{Z^2}{n^2}.$

For n=5(4th excited state) Z=5. For Z=5 E and n =3(2nd excited state) E is $13.6\ast \frac{25}{9}=37.77$

Sinece 37.7 > 25 therefore the electron cant be set free .

As all options match except D.

Hence , option D is correct .