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

Question

If the first excitation potential of a hypothetical hydrogen like atom is 15 V, then the third excitation potential of the atom is (A) 13.6 V (B) (4/75) V (C) (15/16) V (D) (75/4) V

Tardigrade Admin · Accepted Answer

Let total energy of hydrogen like atom at ground state

= - E

So, 1 st excitation
Energy

= E_{2 n d} - E_{1 s t}

15 e V = (\frac{- E}{2 ^{2}}) - [\frac{E}{1 ^{2}}]

(∵

First excitation potential is given)

\Rightarrow \frac{3 E}{4} = 15 e V

\Rightarrow E = \frac{15 \times 4}{3} e V = 20 e V

Now, the third excitation energy

E_{3} = E_{4^{t h}} - E_{1^{s t}}

= (\frac{- E}{4 ^{2}}) - [\frac{E}{1 ^{2}}]

E_{3} = + \frac{15 E}{16}

Now, putting the value of

E

, we get

E_{3} = \frac{15}{16} \times 20 = \frac{75}{4} e V

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

$13.6 V$

$\frac{4}{75} V$

$\frac{15}{16} V$

$\frac{75}{4} V$

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

13.6V

754​V

1615​V

475​V

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

$13.6 V$

$\frac{4}{75} V$

$\frac{15}{16} V$

$\frac{75}{4} V$