Question

In a hydrogen – like hypothetical atom, ionization energy is 12 ev. first excitation energy for such an atom is
A. 3 ev
B. 8.6 ev
C. 9.0 ev
D. 9.8 ev

Answer 1

Hint :To solve this question firstly we have to use the ionization energy formula for the hydrogen like species and after that putting the ionization energy is equal to 12 electron volt and atomic number of hydrogen atom is 1 also first excitation means shell is equal to 2 . Finally we get the first excitation energy.

Complete Step By Step Answer:
As we all know that for , hydrogen like atom ionization energy is 12 ev(given)
Now we will write the formula for ionization energy:
By formula :
I.E. = $ \dfrac{{{Z^2}}}{{{n^2}}} \times 13.6ev/atom $
But according to given condition ionization energy is 12 ev
So after putting the value of 12 ev in equation:
I.E. = $ \dfrac{{{Z^2}}}{{{n^2}}} \times 12ev/atom $
For hydrogen like species z =1 always.
And for first excitation n=2
So after putting all values:
First excitation energy will be:
 $
   \Rightarrow \dfrac{1}{{{2^2}}} \times 12 \\
   \Rightarrow \dfrac{1}{4} \times 12 \\
   \Rightarrow 3 \\
  $
Hence, first excitation energy will be of 3ev per atom
Therefore the correct option is A.

Note :
Ionization energy the energy required to completely extract an electron from an atom in gaseous phase is known as ionization energy of the atom
Excitation energy: it is defined as the energy required to excite an electron from lower energy level to higher energy level in an atom.