If the first excitation potential of a hypothetical hydrogen like atom is 15 V, then the third excitation potential of the atom is

Options

A. 13.6 V
B. `(4)/(75)` V
C. `(15)/(16) ` V
D. `(75)/(4)` V

Answer

A

Explanation

Let total energy of hydrogen like atom at ground state = -E
So, 1st excitation
Energy `= E_(2nd) - E_(1st)`
`15 eV = ((-E)/(2^(2))) - [(E)/(1^(2))]`
(`because` First excitation potential is given)
`rArr (3E)/(4) = 15 eV`
`rArr E = (15 xx 4)/(3) eV = 20 eV`
Now, the third excitation energy
`E_(3) = E_(4^(th)) - E_(1^(st))`
`= ((-E)/(4^(2))) - [(E)/(1^(2))]`
`E_(3) = + (15 E)/(16)`
Now, putting the value of E, get
`E_(3) = (15)/(16) xx 20 = (75)/(4) eV`
Hence, the correct option is (d).